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Results tagged with homological-algebra
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user 161009
(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.
6
votes
Accepted
Geometric interpretation of shuffle product
Perhaps this is more naïve than you are looking for, but here is one interpretation: one representation of an $n$ simplex is the following
$$\Delta_n=\{(t_1,t_2,\dotsc,t_n)\mid 0\leq t_1\leq t_2\leq\d …
- 518
6
votes
1
answer
353
views
Comparing Hochschild (co)homology for algebras and coalgebras
Given a field $k$, an associative $k$-algebra $A$, and an $A$-bimodule $M$, one can define as the Hochschild homology and cohomology as the homology of the complexes
$$M\otimes A^{\otimes n}$$
and
$$\ …
- 518
2
votes
Comparing Hochschild (co)homology for algebras and coalgebras
We assume $A$ and $M$ are finite dimensional, and denote by $A*$ and $M*$ their respective duals. Denote by $HH_n$ and $CH_n$ the Hochschild homology of an algebra and a coalgebra respectively, and si …
- 518