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Results tagged with homological-algebra
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user 128371
(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.
3
votes
1
answer
185
views
Spherical objects and K-theory
My question goes as follows: given a ring $R$ (with $1\neq 0$). Define $\mathbf{Perf}_{R}$ the the category of Prefect complexes over $R$. I want to prove that the Waldhausen $K$-theory of the categor …
- 511
4
votes
1
answer
193
views
Split cofibrations up to quasi-isomorphism
$R$ a ring $(1\neq 0)$, $\mathbf{Perf}(R)$ is the category of perfect complexes (of right $R$-modules).
Suppose that $A_{\bullet}\rightarrow B_{\bullet}\rightarrow B_{\bullet}/A_{\bullet}$ a short e …
- 511
3
votes
1
answer
125
views
Smallness condition for augmented algebras
I'm not sure this question is research level question. Sorry in advance.
Hypothesis
$k$ is a commutative ring.
$A$ is an augmented $k$-algebra.
$A^e$ is defined as the $k$-algebra $A\otimes_{k}A^{op} …
- 511