Author | Popescu, Nicolae. author |
---|---|
Title | Theory of categories [electronic resource] / by Nicolae Popescu, Liliana Popescu |
Imprint | Dordrecht : Springer Netherlands, 1979 |
Connect to | http://dx.doi.org/10.1007/978-94-009-9550-5 |
Descript | X, 338 p. online resource |
1 Categories and Functors -- 1.1. The notion of a category. Examples. Duality -- 1.2. Special morphisms in a category -- 1.3. Functors -- 1.4. Equivalence of categories -- 1.5. Equivalence relations on a category -- 1.6. Limits and colimits -- 1.7. Products and coproducts -- 1.8. Some special limits and colimits -- 1.9. Existence of limits and colimits -- 1.10. Limits and colimits in the category of functors -- 1.11. Adjoint functors -- 1.12. Commutation of functors with limits and colimits -- 1.13. Categories of fractions -- 1.14. Calculus of fractions -- 1.15. Existence of a coadjoint to the canonical functor P: ? ? ? (?-1) -- 1.16. Subobjects and quotient objects -- 1.17. Intersections and unions of subobjects -- 1.18. Images and inverse images -- 1.19. Triangular decomposition of morphisms -- 1.20. Relative triangular decomposition of morphisms -- 2 Completion of Categories -- 2.1. Proper functors -- 2.2. The extension theorem -- 2.3. Dense functors -- 2.4. ?-sheaves -- 2.5. Topologies and sheaves -- 2.6. Some adjoint theorems -- 2.7. A generalization of the extension theorem -- 2.8. Completion of categories -- 2.9. Grothendieck topologies -- 3 Algebraic Categories -- 3.1. Algebraic theories -- 3.2. Algebraic categories -- 3.3. Algebraic functors -- 3.4. Coalgebras -- 3.5. Characterization of algebraic categories -- 4 Abelian Categories -- 4.1. Preadditive and additive categories -- 4.2. Abelian categories -- 4.3. The isomorphism theorems -- 4.4. Limits and colimits in abelian categories -- 4.5. The extension theorem in the additive case. A characterization of functor categories -- 4.6. Injective objects in abelian categories -- 4.7. Categories of additive fractions -- 4.8. Left exact functors. The embedding theorem -- References