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Results tagged with homological-algebra
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user 8032
(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.
11
votes
Homotopy classification of selfmaps of product of spheres?
No chance. For example, take the self maps of $S^3 \times S^3$. Then based maps gives
$$
\text{maps}_\ast(S^3\times S^3,S^3 \times S^3) = \text{maps}_\ast(S^3\times S^3,S^3) \times \text{maps}_\ast(S …
- 18.5k
6
votes
Accepted
How do I split a homotopy idempotent?
Let me re-denote your chain complex $a$ by $C$. You can define a chain complex $D$ as the mapping telescope of the infinite sequence
$$
\cdots\overset e\to \quad C \quad \overset e\to \quad C \quad \o …
- 18.5k
8
votes
Poincare duality and the $A_\infty$ structure on cohomology
Jeffrey,
Nathaniel's 3) above is important to emphasize: a (homology) manifold is a space which satisfies local Poincare duality, i.e., it is some sort of sheaf of self dual complexes, whereas a Poi …
- 18.5k
1
vote
Spherical objects and K-theory
I believe the theorem you are trying to prove is due to Brinkmann who was an early student of Waldhausen.
What you are suggesting as the proof is only part of the story.
In addition to section 1.7 …
- 18.5k