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Seminar on Category Theory and Homological Algebra

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2020-03-31 14:38:28
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CUHK self study group. C for category, H for homological algebra, numbers are in chronological order See comments or personal updates for full set of materials.
视频教程
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数学
公开课
homological algebra
category theory
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C1. categories, functors
01:06:57
C2.1 Natural transformations
31:15
C2.2 Equivalence of Categories definitions
32:55
C3. Equivalence of categories proof of 2.5
01:37:28
C4. Equivalence of Categories proof of 2.7 except (ii) to (iii)
55:32
C5.1. Equivalence of Categories proof of 2.7 (ii) to (iii)
58:10
C5.2. Equivalence of Categories proof of 2.7 (ii) to (iii) tedious check
17:57
C6. Equivalence of Categories 2.7 cont'd,Example,adjoints via unit and counit.
44:49
C7. definition via natural transformation, proof two def are equivalent
31:52
C8. proof of right adjoint is unique
46:32
C9. examples of adjunction, product of categories
28:45
C10. product of categories
01:29:12
C11. Functor category, Category of small categories
01:15:24
C12. Comma category
48:18
C13. category of small graphs
38:34
C14. free category, tensor product of modules
01:29:40
C15. tensor product of modules
01:16:26
C15.2 two equivalent definition of tensor products
28:54
C16. Tensor product over a commutative ring
01:21:24
C17. definition of tensor, symmetric and exterior algebras
56:28
C18. tensor algebra properties, symmetric algebra
01:18:31
C19. coproduct in category of super algebras
41:56
C20. exterior algebra (cont), relationship between three algebras
01:40:43
C21. Ex of free-forgetful adjuctions,change of coefficients, abelianization
01:50:40
C22. Eg free-forgetful adjuctions, monoid ring, fraction field,galois connection
01:50:17
C23. The Hom-tensor adjunction
02:26:29
C24. Hom-tensor adjuction for opposite rings, tensor functors are right exact
02:08:33
H25. Category of R-Mod, monics and epics
01:49:44
C26. Hom is left exact, tensor and hom commute with products or coproducts
01:50:13
H27. product and coproduct in R-Mod, free and projective modules
01:52:13
H28. Hom interects with product and coproduct, universals
01:25:50
H29. proof of additive functor=preservation of biproduct, projective modules
02:05:54
C30. Yoneda embedding, yoneda lemma
01:23:35
H31. Dual basis theorem for projective modules
38:01
C32. yoneda lemma cor, eg cayley thm, covariant and contravariant version
01:22:03
H33. flat modules
36:12
C34. Adjoint via universal and representable functors
02:23:37
C35. Left adjoint implies universals
01:17:43
H36. flat module over commutative rings
43:27
C37. Contravariant version of 2.6, def of Limit
01:08:37
H38. Flatness examples, injective module
45:16
C39. Revision 1
01:06:29
H40. baers criterion, divisible module
01:07:54
H41. Injective imbedding theorem, injective hull
01:50:42
C42. Limits and examples
01:05:51
H43. Example of Injective Modules
36:29
C44. Eg of limits
01:16:39
H45. Morita context def
01:27:05
C46. Colimit, categorical duality
01:40:12
C47. Completeness
01:04:59
H48. Morita I
01:12:32
C49. Filtered limits, completeness
01:00:15
H50. Morita I, progenerator
53:20
H51. Generators and progenerators
01:28:34
H52. Morita II, III
52:43
C53. Regular monics and epis, def of creation of limit
01:23:08
H54. Kernels and cokernels, preadditive category
01:39:26
C55. Creation, reflection, perservation of limits
01:54:35
H56. Additive Categories
01:29:01

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