Squared Hopf Algebras.

Intro -- Contents -- Introduction -- Chapter 1. Tools -- 1.1. Tensor product of abelian categories -- 1.2. Monoidal categories -- 1.3. Monoidal abelian categories -- 1.4. Symmetric monoidal 2-category of abelian categories -- 1.5. System of notations -- 1.6. Monoidal structures on V [omitted] V -- 1.7. Ind-objects -- 1.8. Rigid-abelian categories -- Chapter 2. Squared coalgebras -- 2.1. Definitions -- 2.2. Comodules -- 2.3. The fundamental theorem on coalgebras -- 2.4. Relationship between categories of comodules -- 2.5. The category of fibre functors -- 2.6. Reconstruction theorems -- 2.7. Comodules over ordinary coalgebras -- 2.8. Construction data -- Chapter 3. Squared bicoalgebras -- 3.1. Tensor product of squared coalgebras -- 3.2. Bicoalgebras -- 3.3. Monoidal construction data -- 3.4. Tensor generators and relations -- 3.5. Relationship with braided bialgebras -- 3.6. Commutative algebras and braiding -- Chapter 4. Hopf coalgebras -- 4.1. Opposite coalgebras -- 4.2. Comparison with opposite coalgebra in braided case -- 4.3. The antipode -- 4.4. Comparison with braided Hopf algebras -- 4.5. Multiplication in the opposite bialgebra -- 4.6. Reconstruction of rigid monoidal categories -- Chapter 5. Quasitriangular Hopf coalgebras -- 5.1. R-matrices in Hopf coalgebras -- 5.2. Braiding for comodules over a braided Hopf algebra -- 5.3. Constructing braided categories -- 5.4. Ribbon Hopf coalgebras -- 5.5. Ribbon reconstruction -- Appendix A. Symmetric monoidal 2-categories -- A.1. A review of 2-categories -- A.2. 2-pasting schemes -- A.3. Weak 2-pasting -- A.4. Weak 3-categories -- A.5. A monoidal 2-category of abelian categories -- A.6. Symmetric monoidal 2-categories -- A.7. A symmetric monoidal 2-category of abelian categories -- Bibliography.

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