Symmetric monoidal 2-category of abelian categories
24
(1)
System of notations
24
(8)
Monoidal structures on V ⊠ V
32
(2)
Ind-objects
34
(3)
Rigid-abelian categories
37
(6)
Squared coalgebras
43
(22)
Definitions
43
(4)
Comodules
47
(1)
The fundamental theorem on coalgebras
48
(2)
Relationship between categories of comodules
50
(1)
The category of fibre functors
51
(4)
Reconstruction theorems
55
(5)
Comodules over ordinary coalgebras
60
(1)
Construction data
61
(4)
Squared bicoalgebras
65
(22)
Tensor product of squared coalgebras
65
(3)
Bicoalgebras
68
(1)
Monoidal construction data
69
(8)
Tensor generators and relations
77
(5)
Relationship with braided bialgebras
82
(3)
Commutative algebras and braiding
85
(2)
Hopf coalgebras
87
(34)
Opposite coalgebras
87
(4)
Comparison with opposite coalgebra in braided case
91
(1)
The antipode
92
(11)
Comparison with braided Hopf algebras
103
(2)
Multiplication in the opposite bialgebra
105
(11)
Reconstruction of rigid monoidal categories
116
(5)
Quasitriangular Hopf coalgebras
121
(13)
R-matrices in Hopf coalgebras
121
(5)
Braiding for comodules over a braided Hopf algebra
126
(1)
Constructing braided categories
127
(2)
Ribbon Hopf coalgebras
129
(2)
Ribbon reconstruction
131
(3)
Appendix A. Symmetric monoidal 2-categories
134
(45)
A.1. A review of 2-categories
134
(2)
A.2. 2-pasting schemes
136
(5)
A.3. Weak 2-pasting
141
(7)
A.4. Weak 3-categories
148
(2)
A.5. A monoidal 2-category of abelian categories
150
(23)
A.6. Symmetric monoidal 2-categories
173
(2)
A.7. A symmetric monoidal 2-category of abelian categories
175
(4)
Bibliography
179
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