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Results tagged with homological-algebra
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user 7041
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
7
votes
2
answers
624
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Why depth, dimension, etc?
Recently I came across a paper by Stephen McAdam "GRADE SCHEMES AND GRADE FUNCTIONS" (Transactions of the American Mathematical Society, Vol. 288, No. 2 (Apr., 1985), pp.
563-590). So far I have just …
- 607
0
votes
Cone of a morphism in an abelian category when considered as a morphism in derived category....
Not a real answer, but hopefully a relevant comment:
There is s very close analogy between the homotopy category of spaces and chain complexes.
You can find such presentation in Peter May's notes on …
- 607
3
votes
1
answer
722
views
Resolutions by Adapted Class of Objects and Model Categories
My question is about the construction of derived functor in the language of model categories. (As it is done for example the paper by Dwyer and Spalinski "Homotopy Theories and Model Categories".) I'v …
- 607
3
votes
0
answers
209
views
Closed Model Category Structure on Chain Complexes Related to A Left-exact Functor
Let $F:A \to B$ be an additive left-exact functor of abelian categories (Do not assume that they have enough injectives / projectives.) Suppose we are given a class of objects $R$ adapted to $F$ (see …
- 607