张量范畴（影印版）
定价：￥169.00
作者： Pavel Etingof，Shlomo Gelaki，Dmitri Nikshych等
出版社：高等教育出版社
- 高等教育出版社
- 9787040661309
- 1版
- 64270572-7
- 特殊
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
前辅文
Preface
Chapter 1. Abelian categories
1.1. Categorical prerequisites and notation
1.2. Additive categories
1.3. Definition of abelian category
1.4. Exact sequences
1.5. Length of objects and the Jordan-H¨older theorem
1.6. Projective and injective objects
1.7. Higher Ext groups and group cohomology
1.8. Locally finite (artinian) and finite abelian categories
1.9. Coalgebras
1.10. The Coend construction
1.11. Deligne’s tensor product of locally finite abelian categories
1.12. The finite dual of an algebra
1.13. Pointed coalgebras and the coradical filtration
1.14. Bibliographical notes
Chapter 2. Monoidal categories
2.1. Definition of a monoidal category
2.2. Basic properties of unit objects
2.3. First examples of monoidal categories
2.4. Monoidal functors and their morphisms
2.5. Examples of monoidal functors
2.6. Monoidal functors between categories of graded vector spaces
2.7. Group actions on categories and equivariantization
2.8. The Mac Lane strictness theorem
2.9. The coherence theorem
2.10. Rigid monoidal categories
2.11. Invertible objects and Gr-categories
2.12. 2-categories
2.13. Bibliographical notes
Chapter 3. Z+-rings
3.1. Definition of a Z+-ring
3.2. The Frobenius-Perron theorem
3.3. The Frobenius-Perron dimensions
3.4. Z+-modules
3.5. Graded based rings
3.6. The adjoint based subring and universal grading
3.7. Complexified Z+-rings and ∗-algebras
3.8. Weak based rings
3.9. Bibliographical notes
Chapter 4. Tensor categories
4.1. Tensor and multitensor categories
4.2. Exactness of the tensor product
4.3. Semisimplicity of the unit object
4.4. Absence of self-extensions of the unit object
4.5. Grothendieck ring and Frobenius-Perron dimension
4.6. Deligne’s tensor product of tensor categories
4.7. Quantum traces, pivotal and spherical categories
4.8. Semisimple multitensor categories
4.9. Grothendieck rings of semisimple tensor categories
4.10. Categorification of based rings
4.11. Tensor subcategories
4.12. Chevalley property of tensor categories
4.13. Groupoids
4.14. The adjoint subcategory and universal grading
4.15. Equivariantization of tensor categories
4.16. Multitensor categories over arbitrary fields
4.17. Bibliographical notes
Chapter 5. Representation categories of Hopf algebras
5.1. Fiber functors
5.2. Bialgebras
5.3. Hopf algebras
5.4. Reconstruction theory in the infinite setting
5.5. More examples of Hopf algebras
5.6. The quantum group Uq(sl2)
5.7. The quantum group Uq(g)
5.8. Representations of quantum groups and quantum function algebras
5.9. Absence of primitive elements
5.10. The Cartier-Gabriel-Kostant theorem
5.11. Pointed tensor categories and Hopf algebras
5.12. Quasi-bialgebras
5.13. Quasi-bialgebras with an antipode and quasi-Hopf algebras
5.14. Twists for bialgebras and Hopf algebras
5.15. Bibliographical notes
5.16. Other results
Chapter 6. Finite tensor categories
6.1. Properties of projective objects
6.2. Categorical freeness
6.3. Injective and surjective tensor functors
6.4. The distinguished invertible object
6.5. Integrals in quasi-Hopf algebras and unimodular categories
6.6. Degeneracy of the Cartan matrix
6.7. Bibliographical notes
Chapter 7. Module categories
7.1. The definition of a module category
7.2. Module functors
7.3. Module categories over multitensor categories
7.4. Examples of module categories
7.5. Exact module categories over finite tensor categories
7.6. First properties of exact module categories
7.7. Module categories and Z+-modules
7.8. Algebras in multitensor categories
7.9. Internal Homs in module categories
7.10. Characterization of module categories in terms of algebras
7.11. Categories of module functors
7.12. Dual tensor categories and categorical Morita equivalence
7.13. The center construction
7.14. The quantum double construction for Hopf algebras
7.15. Yetter-Drinfeld modules
7.16. Invariants of categorical Morita equivalence
7.17. Duality for tensor functors and Lagrange’s Theorem
7.18. Hopf bimodules and the Fundamental Theorem
7.19. Radford’s isomorphism for the fourth dual
7.20. The canonical Frobenius algebra of a unimodular category
7.21. Categorical dimension of a multifusion category
7.22. Davydov-Yetter cohomology and deformations of tensor categories
7.23. Weak Hopf algebras
7.24. Bibliographical notes
7.25. Other results
Chapter 8. Braided categories
8.1. Definition of a braided category
8.2. First examples of braided categories and functors
8.3. Quasitriangular Hopf algebras
8.4. Pre-metric groups and pointed braided fusion categories
8.5. The center as a braided category
8.6. Factorizable braided tensor categories
8.7. Module categories over braided tensor categories
8.8. Commutative algebras and central functors
8.9. The Drinfeld morphism
8.10. Ribbon monoidal categories
8.11. Ribbon Hopf algebras
8.12. Characterization of Morita equivalence
8.13. The S-matrix of a pre-modular category
8.14. Modular categories
8.15. Gauss sums and the central charge
8.16. Representation of the modular group
8.17. Modular data
8.18. The Anderson-Moore-Vafa property and Verlinde categories
8.19. A non-spherical generalization of the S-matrix
8.20. Centralizers and non-degeneracy
8.21. Dimensions of centralizers
8.22. Projective centralizers
8.23. De-equivariantization
8.24. Braided G-crossed categories
8.25. Braided Hopf algebras, Nichols algebras, pointed Hopf algebras
8.26. Bibliographical notes
8.27. Other results
Chapter 9. Fusion categories
9.1. Ocneanu rigidity (absence of deformations)
9.2. Induction to the center
9.3. Duality for fusion categories
9.4. Pseudo-unitary fusion categories
9.5. Canonical spherical structure
9.6. Integral and weakly integral fusion categories
9.7. Group-theoretical fusion categories
9.8. Weakly group-theoretical fusion categories
9.9. Symmetric and Tannakian fusion categories
9.10. Existence of a fiber functor
9.11. Deligne’s theorem for infinite categories
9.12. The Deligne categories Rep(St), Rep(GLt), Rep(Ot), Rep(Sp2t)
9.13. Recognizing group-theoretical fusion categories
9.14. Fusion categories of prime power dimension
9.15. Burnside’s theorem for fusion categories
9.16. Lifting theory
9.17. Bibliographical notes
9.18. Other results
Bibliography
Index
前辅文
Preface
Chapter 1. Abelian categories
1.1. Categorical prerequisites and notation
1.2. Additive categories
1.3. Definition of abelian category
1.4. Exact sequences
1.5. Length of objects and the Jordan-H¨older theorem
1.6. Projective and injective objects
1.7. Higher Ext groups and group cohomology
1.8. Locally finite (artinian) and finite abelian categories
1.9. Coalgebras
1.10. The Coend construction
1.11. Deligne’s tensor product of locally finite abelian categories
1.12. The finite dual of an algebra
1.13. Pointed coalgebras and the coradical filtration
1.14. Bibliographical notes
Chapter 2. Monoidal categories
2.1. Definition of a monoidal category
2.2. Basic properties of unit objects
2.3. First examples of monoidal categories
2.4. Monoidal functors and their morphisms
2.5. Examples of monoidal functors
2.6. Monoidal functors between categories of graded vector spaces
2.7. Group actions on categories and equivariantization
2.8. The Mac Lane strictness theorem
2.9. The coherence theorem
2.10. Rigid monoidal categories
2.11. Invertible objects and Gr-categories
2.12. 2-categories
2.13. Bibliographical notes
Chapter 3. Z+-rings
3.1. Definition of a Z+-ring
3.2. The Frobenius-Perron theorem
3.3. The Frobenius-Perron dimensions
3.4. Z+-modules
3.5. Graded based rings
3.6. The adjoint based subring and universal grading
3.7. Complexified Z+-rings and ∗-algebras
3.8. Weak based rings
3.9. Bibliographical notes
Chapter 4. Tensor categories
4.1. Tensor and multitensor categories
4.2. Exactness of the tensor product
4.3. Semisimplicity of the unit object
4.4. Absence of self-extensions of the unit object
4.5. Grothendieck ring and Frobenius-Perron dimension
4.6. Deligne’s tensor product of tensor categories
4.7. Quantum traces, pivotal and spherical categories
4.8. Semisimple multitensor categories
4.9. Grothendieck rings of semisimple tensor categories
4.10. Categorification of based rings
4.11. Tensor subcategories
4.12. Chevalley property of tensor categories
4.13. Groupoids
4.14. The adjoint subcategory and universal grading
4.15. Equivariantization of tensor categories
4.16. Multitensor categories over arbitrary fields
4.17. Bibliographical notes
Chapter 5. Representation categories of Hopf algebras
5.1. Fiber functors
5.2. Bialgebras
5.3. Hopf algebras
5.4. Reconstruction theory in the infinite setting
5.5. More examples of Hopf algebras
5.6. The quantum group Uq(sl2)
5.7. The quantum group Uq(g)
5.8. Representations of quantum groups and quantum function algebras
5.9. Absence of primitive elements
5.10. The Cartier-Gabriel-Kostant theorem
5.11. Pointed tensor categories and Hopf algebras
5.12. Quasi-bialgebras
5.13. Quasi-bialgebras with an antipode and quasi-Hopf algebras
5.14. Twists for bialgebras and Hopf algebras
5.15. Bibliographical notes
5.16. Other results
Chapter 6. Finite tensor categories
6.1. Properties of projective objects
6.2. Categorical freeness
6.3. Injective and surjective tensor functors
6.4. The distinguished invertible object
6.5. Integrals in quasi-Hopf algebras and unimodular categories
6.6. Degeneracy of the Cartan matrix
6.7. Bibliographical notes
Chapter 7. Module categories
7.1. The definition of a module category
7.2. Module functors
7.3. Module categories over multitensor categories
7.4. Examples of module categories
7.5. Exact module categories over finite tensor categories
7.6. First properties of exact module categories
7.7. Module categories and Z+-modules
7.8. Algebras in multitensor categories
7.9. Internal Homs in module categories
7.10. Characterization of module categories in terms of algebras
7.11. Categories of module functors
7.12. Dual tensor categories and categorical Morita equivalence
7.13. The center construction
7.14. The quantum double construction for Hopf algebras
7.15. Yetter-Drinfeld modules
7.16. Invariants of categorical Morita equivalence
7.17. Duality for tensor functors and Lagrange’s Theorem
7.18. Hopf bimodules and the Fundamental Theorem
7.19. Radford’s isomorphism for the fourth dual
7.20. The canonical Frobenius algebra of a unimodular category
7.21. Categorical dimension of a multifusion category
7.22. Davydov-Yetter cohomology and deformations of tensor categories
7.23. Weak Hopf algebras
7.24. Bibliographical notes
7.25. Other results
Chapter 8. Braided categories
8.1. Definition of a braided category
8.2. First examples of braided categories and functors
8.3. Quasitriangular Hopf algebras
8.4. Pre-metric groups and pointed braided fusion categories
8.5. The center as a braided category
8.6. Factorizable braided tensor categories
8.7. Module categories over braided tensor categories
8.8. Commutative algebras and central functors
8.9. The Drinfeld morphism
8.10. Ribbon monoidal categories
8.11. Ribbon Hopf algebras
8.12. Characterization of Morita equivalence
8.13. The S-matrix of a pre-modular category
8.14. Modular categories
8.15. Gauss sums and the central charge
8.16. Representation of the modular group
8.17. Modular data
8.18. The Anderson-Moore-Vafa property and Verlinde categories
8.19. A non-spherical generalization of the S-matrix
8.20. Centralizers and non-degeneracy
8.21. Dimensions of centralizers
8.22. Projective centralizers
8.23. De-equivariantization
8.24. Braided G-crossed categories
8.25. Braided Hopf algebras, Nichols algebras, pointed Hopf algebras
8.26. Bibliographical notes
8.27. Other results
Chapter 9. Fusion categories
9.1. Ocneanu rigidity (absence of deformations)
9.2. Induction to the center
9.3. Duality for fusion categories
9.4. Pseudo-unitary fusion categories
9.5. Canonical spherical structure
9.6. Integral and weakly integral fusion categories
9.7. Group-theoretical fusion categories
9.8. Weakly group-theoretical fusion categories
9.9. Symmetric and Tannakian fusion categories
9.10. Existence of a fiber functor
9.11. Deligne’s theorem for infinite categories
9.12. The Deligne categories Rep(St), Rep(GLt), Rep(Ot), Rep(Sp2t)
9.13. Recognizing group-theoretical fusion categories
9.14. Fusion categories of prime power dimension
9.15. Burnside’s theorem for fusion categories
9.16. Lifting theory
9.17. Bibliographical notes
9.18. Other results
Bibliography
Index
前辅文
Preface
Chapter 1. Abelian categories
1.1. Categorical prerequisites and notation
1.2. Additive categories
1.3. Definition of abelian category
1.4. Exact sequences
1.5. Length of objects and the Jordan-H¨older theorem
1.6. Projective and injective objects
1.7. Higher Ext groups and group cohomology
1.8. Locally finite (artinian) and finite abelian categories
1.9. Coalgebras
1.10. The Coend construction
1.11. Deligne’s tensor product of locally finite abelian categories
1.12. The finite dual of an algebra
1.13. Pointed coalgebras and the coradical filtration
1.14. Bibliographical notes
Chapter 2. Monoidal categories
2.1. Definition of a monoidal category
2.2. Basic properties of unit objects
2.3. First examples of monoidal categories
2.4. Monoidal functors and their morphisms
2.5. Examples of monoidal functors
2.6. Monoidal functors between categories of graded vector spaces
2.7. Group actions on categories and equivariantization
2.8. The Mac Lane strictness theorem
2.9. The coherence theorem
2.10. Rigid monoidal categories
2.11. Invertible objects and Gr-categories
2.12. 2-categories
2.13. Bibliographical notes
Chapter 3. Z+-rings
3.1. Definition of a Z+-ring
3.2. The Frobenius-Perron theorem
3.3. The Frobenius-Perron dimensions
3.4. Z+-modules
3.5. Graded based rings
3.6. The adjoint based subring and universal grading
3.7. Complexified Z+-rings and ∗-algebras
3.8. Weak based rings
3.9. Bibliographical notes
Chapter 4. Tensor categories
4.1. Tensor and multitensor categories
4.2. Exactness of the tensor product
4.3. Semisimplicity of the unit object
4.4. Absence of self-extensions of the unit object
4.5. Grothendieck ring and Frobenius-Perron dimension
4.6. Deligne’s tensor product of tensor categories
4.7. Quantum traces, pivotal and spherical categories
4.8. Semisimple multitensor categories
4.9. Grothendieck rings of semisimple tensor categories
4.10. Categorification of based rings
4.11. Tensor subcategories
4.12. Chevalley property of tensor categories
4.13. Groupoids
4.14. The adjoint subcategory and universal grading
4.15. Equivariantization of tensor categories
4.16. Multitensor categories over arbitrary fields
4.17. Bibliographical notes
Chapter 5. Representation categories of Hopf algebras
5.1. Fiber functors
5.2. Bialgebras
5.3. Hopf algebras
5.4. Reconstruction theory in the infinite setting
5.5. More examples of Hopf algebras
5.6. The quantum group Uq(sl2)
5.7. The quantum group Uq(g)
5.8. Representations of quantum groups and quantum function algebras
5.9. Absence of primitive elements
5.10. The Cartier-Gabriel-Kostant theorem
5.11. Pointed tensor categories and Hopf algebras
5.12. Quasi-bialgebras
5.13. Quasi-bialgebras with an antipode and quasi-Hopf algebras
5.14. Twists for bialgebras and Hopf algebras
5.15. Bibliographical notes
5.16. Other results
Chapter 6. Finite tensor categories
6.1. Properties of projective objects
6.2. Categorical freeness
6.3. Injective and surjective tensor functors
6.4. The distinguished invertible object
6.5. Integrals in quasi-Hopf algebras and unimodular categories
6.6. Degeneracy of the Cartan matrix
6.7. Bibliographical notes
Chapter 7. Module categories
7.1. The definition of a module category
7.2. Module functors
7.3. Module categories over multitensor categories
7.4. Examples of module categories
7.5. Exact module categories over finite tensor categories
7.6. First properties of exact module categories
7.7. Module categories and Z+-modules
7.8. Algebras in multitensor categories
7.9. Internal Homs in module categories
7.10. Characterization of module categories in terms of algebras
7.11. Categories of module functors
7.12. Dual tensor categories and categorical Morita equivalence
7.13. The center construction
7.14. The quantum double construction for Hopf algebras
7.15. Yetter-Drinfeld modules
7.16. Invariants of categorical Morita equivalence
7.17. Duality for tensor functors and Lagrange’s Theorem
7.18. Hopf bimodules and the Fundamental Theorem
7.19. Radford’s isomorphism for the fourth dual
7.20. The canonical Frobenius algebra of a unimodular category
7.21. Categorical dimension of a multifusion category
7.22. Davydov-Yetter cohomology and deformations of tensor categories
7.23. Weak Hopf algebras
7.24. Bibliographical notes
7.25. Other results
Chapter 8. Braided categories
8.1. Definition of a braided category
8.2. First examples of braided categories and functors
8.3. Quasitriangular Hopf algebras
8.4. Pre-metric groups and pointed braided fusion categories
8.5. The center as a braided category
8.6. Factorizable braided tensor categories
8.7. Module categories over braided tensor categories
8.8. Commutative algebras and central functors
8.9. The Drinfeld morphism
8.10. Ribbon monoidal categories
8.11. Ribbon Hopf algebras
8.12. Characterization of Morita equivalence
8.13. The S-matrix of a pre-modular category
8.14. Modular categories
8.15. Gauss sums and the central charge
8.16. Representation of the modular group
8.17. Modular data
8.18. The Anderson-Moore-Vafa property and Verlinde categories
8.19. A non-spherical generalization of the S-matrix
8.20. Centralizers and non-degeneracy
8.21. Dimensions of centralizers
8.22. Projective centralizers
8.23. De-equivariantization
8.24. Braided G-crossed categories
8.25. Braided Hopf algebras, Nichols algebras, pointed Hopf algebras
8.26. Bibliographical notes
8.27. Other results
Chapter 9. Fusion categories
9.1. Ocneanu rigidity (absence of deformations)
9.2. Induction to the center
9.3. Duality for fusion categories
9.4. Pseudo-unitary fusion categories
9.5. Canonical spherical structure
9.6. Integral and weakly integral fusion categories
9.7. Group-theoretical fusion categories
9.8. Weakly group-theoretical fusion categories
9.9. Symmetric and Tannakian fusion categories
9.10. Existence of a fiber functor
9.11. Deligne’s theorem for infinite categories
9.12. The Deligne categories Rep(St), Rep(GLt), Rep(Ot), Rep(Sp2t)
9.13. Recognizing group-theoretical fusion categories
9.14. Fusion categories of prime power dimension
9.15. Burnside’s theorem for fusion categories
9.16. Lifting theory
9.17. Bibliographical notes
9.18. Other results
Bibliography
Index
前辅文
Preface
Chapter 1. Abelian categories
1.1. Categorical prerequisites and notation
1.2. Additive categories
1.3. Definition of abelian category
1.4. Exact sequences
1.5. Length of objects and the Jordan-H¨older theorem
1.6. Projective and injective objects
1.7. Higher Ext groups and group cohomology
1.8. Locally finite (artinian) and finite abelian categories
1.9. Coalgebras
1.10. The Coend construction
1.11. Deligne’s tensor product of locally finite abelian categories
1.12. The finite dual of an algebra
1.13. Pointed coalgebras and the coradical filtration
1.14. Bibliographical notes
Chapter 2. Monoidal categories
2.1. Definition of a monoidal category
2.2. Basic properties of unit objects
2.3. First examples of monoidal categories
2.4. Monoidal functors and their morphisms
2.5. Examples of monoidal functors
2.6. Monoidal functors between categories of graded vector spaces
2.7. Group actions on categories and equivariantization
2.8. The Mac Lane strictness theorem
2.9. The coherence theorem
2.10. Rigid monoidal categories
2.11. Invertible objects and Gr-categories
2.12. 2-categories
2.13. Bibliographical notes
Chapter 3. Z+-rings
3.1. Definition of a Z+-ring
3.2. The Frobenius-Perron theorem
3.3. The Frobenius-Perron dimensions
3.4. Z+-modules
3.5. Graded based rings
3.6. The adjoint based subring and universal grading
3.7. Complexified Z+-rings and ∗-algebras
3.8. Weak based rings
3.9. Bibliographical notes
Chapter 4. Tensor categories
4.1. Tensor and multitensor categories
4.2. Exactness of the tensor product
4.3. Semisimplicity of the unit object
4.4. Absence of self-extensions of the unit object
4.5. Grothendieck ring and Frobenius-Perron dimension
4.6. Deligne’s tensor product of tensor categories
4.7. Quantum traces, pivotal and spherical categories
4.8. Semisimple multitensor categories
4.9. Grothendieck rings of semisimple tensor categories
4.10. Categorification of based rings
4.11. Tensor subcategories
4.12. Chevalley property of tensor categories
4.13. Groupoids
4.14. The adjoint subcategory and universal grading
4.15. Equivariantization of tensor categories
4.16. Multitensor categories over arbitrary fields
4.17. Bibliographical notes
Chapter 5. Representation categories of Hopf algebras
5.1. Fiber functors
5.2. Bialgebras
5.3. Hopf algebras
5.4. Reconstruction theory in the infinite setting
5.5. More examples of Hopf algebras
5.6. The quantum group Uq(sl2)
5.7. The quantum group Uq(g)
5.8. Representations of quantum groups and quantum function algebras
5.9. Absence of primitive elements
5.10. The Cartier-Gabriel-Kostant theorem
5.11. Pointed tensor categories and Hopf algebras
5.12. Quasi-bialgebras
5.13. Quasi-bialgebras with an antipode and quasi-Hopf algebras
5.14. Twists for bialgebras and Hopf algebras
5.15. Bibliographical notes
5.16. Other results
Chapter 6. Finite tensor categories
6.1. Properties of projective objects
6.2. Categorical freeness
6.3. Injective and surjective tensor functors
6.4. The distinguished invertible object
6.5. Integrals in quasi-Hopf algebras and unimodular categories
6.6. Degeneracy of the Cartan matrix
6.7. Bibliographical notes
Chapter 7. Module categories
7.1. The definition of a module category
7.2. Module functors
7.3. Module categories over multitensor categories
7.4. Examples of module categories
7.5. Exact module categories over finite tensor categories
7.6. First properties of exact module categories
7.7. Module categories and Z+-modules
7.8. Algebras in multitensor categories
7.9. Internal Homs in module categories
7.10. Characterization of module categories in terms of algebras
7.11. Categories of module functors
7.12. Dual tensor categories and categorical Morita equivalence
7.13. The center construction
7.14. The quantum double construction for Hopf algebras
7.15. Yetter-Drinfeld modules
7.16. Invariants of categorical Morita equivalence
7.17. Duality for tensor functors and Lagrange’s Theorem
7.18. Hopf bimodules and the Fundamental Theorem
7.19. Radford’s isomorphism for the fourth dual
7.20. The canonical Frobenius algebra of a unimodular category
7.21. Categorical dimension of a multifusion category
7.22. Davydov-Yetter cohomology and deformations of tensor categories
7.23. Weak Hopf algebras
7.24. Bibliographical notes
7.25. Other results
Chapter 8. Braided categories
8.1. Definition of a braided category
8.2. First examples of braided categories and functors
8.3. Quasitriangular Hopf algebras
8.4. Pre-metric groups and pointed braided fusion categories
8.5. The center as a braided category
8.6. Factorizable braided tensor categories
8.7. Module categories over braided tensor categories
8.8. Commutative algebras and central functors
8.9. The Drinfeld morphism
8.10. Ribbon monoidal categories
8.11. Ribbon Hopf algebras
8.12. Characterization of Morita equivalence
8.13. The S-matrix of a pre-modular category
8.14. Modular categories
8.15. Gauss sums and the central charge
8.16. Representation of the modular group
8.17. Modular data
8.18. The Anderson-Moore-Vafa property and Verlinde categories
8.19. A non-spherical generalization of the S-matrix
8.20. Centralizers and non-degeneracy
8.21. Dimensions of centralizers
8.22. Projective centralizers
8.23. De-equivariantization
8.24. Braided G-crossed categories
8.25. Braided Hopf algebras, Nichols algebras, pointed Hopf algebras
8.26. Bibliographical notes
8.27. Other results
Chapter 9. Fusion categories
9.1. Ocneanu rigidity (absence of deformations)
9.2. Induction to the center
9.3. Duality for fusion categories
9.4. Pseudo-unitary fusion categories
9.5. Canonical spherical structure
9.6. Integral and weakly integral fusion categories
9.7. Group-theoretical fusion categories
9.8. Weakly group-theoretical fusion categories
9.9. Symmetric and Tannakian fusion categories
9.10. Existence of a fiber functor
9.11. Deligne’s theorem for infinite categories
9.12. The Deligne categories Rep(St), Rep(GLt), Rep(Ot), Rep(Sp2t)
9.13. Recognizing group-theoretical fusion categories
9.14. Fusion categories of prime power dimension
9.15. Burnside’s theorem for fusion categories
9.16. Lifting theory
9.17. Bibliographical notes
9.18. Other results
Bibliography
Index
