Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with homological-algebra
Search options answers only
not deleted
user 102343
(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.
4
votes
Accepted
Checking exactness of a triangle on stalks
The answer is no, but we can say a bit more : it can become true if you pass to the derived $\infty$-category and replace the words "distinguished triangle" with "cofiber sequence" (modulo the choice …
- 15.7k
5
votes
Comparing the Stacks Project Homotopy limit with limits in the $\infty$-category
There is a reference for this in Lurie's Higher topos theory - specifically, see Theorem 4.2.4.1, Corollary 4.2.4.8.
The key to these is Proposition 4.2.4.4, which itself relies heavily on Appendix A …
- 15.7k
6
votes
Can not tell colimits from limits
EDIT: The main body of my answer is there because I didn't understand the question, so let me answer it in this edit (I'll leave the main body of the answer there, just in case)
No, there is no typo …
- 15.7k
9
votes
Accepted
Is the class of isomorphism types of a module category always a set?
Yes, because you're only considering finitely generated modules. No assumptions on $A$ are required.
Indeed, a finitely generated module is always a quotient of some $A^n$ by some submodule. For each …
- 15.7k
2
votes
Accepted
Epimorphism going out of an inverse limit into a finite dimensional module
The answer is no. First, let me point out that the $A$ here plays no role: because each $M_{i+1}\to M_i$ is an epimorphism, $M\to M_i$ is one too, and so if there is a $k$-linear factorization $M\to M …
- 15.7k
7
votes
Accepted
Does $\mathrm{Ind}(\mathcal{C})$ have enough injectives, if $\mathcal{C}$ is an abelian cate...
As Dan Petersen said in the comments, $Mod(k)$ isn't small. Note that even in this case, $Ind(Mod(k))$ only has small direct sums, and in particular you cannot take the direct sum that appears in poin …
- 15.7k
5
votes
Accepted
Adjunctions and inverse limits of derived categories
A reference for exactly this type of problem in general is a paper by Horev and Yanovski called "On conjugates and adjoint descent".
Given a diagram $C \to D_i$ of left adjoints $f_i$ with right adjoi …
- 15.7k
3
votes
Accepted
Linearity of topological periodic cyclic homology
If you want a full module structure (rather than just an "action map" $TP(A)\otimes TP(B)\to TP(B)$, which is enough for some arguments), the reasonable notion would be for $B$ to be an $A$-module in …
- 15.7k
11
votes
How many tensor products of chain complexes are there?
tldr: (but also, spoilers !) If you impose the further condition that chain complexes be a $Gr$-algebra, then there is a unique monoidal structure - which one of your two options it is will depend on …
- 15.7k
5
votes
Accepted
Derived functor of functor tensor product
The answer is yes if you assume enough things. In particular, the notion of a left flat object of $\mathcal A$ comes up :
Definition: An object $L\in\mathcal A$ is left flat if $-\otimes L$ is exact.
…
- 15.7k
6
votes
Difference between $K(1)$-local K theory and l-adic completion of etale $K$ theory
Yes, there is a map: by Thomason's work, $L_{K(1)}K$ satisfies étale descent and the canonical map $K\to L_{K(1)}K$ therefore induces a canonical map $K^{ét}\to L_{K(1)}K$.
This paper by Clausen and M …
- 15.7k
3
votes
Accepted
A non-projective rigid object in an abelian monoidal category
If by "rigid" you mean the same thing as dualizable, an example is given by $\mathcal M = Mod_{R[G]}$ for some commutative ring $R$ and group $G$, with monoidal structure given by $\otimes_R$ and the …
- 15.7k
5
votes
Accepted
$\mathbb{Z}$-homomorphism and $\mathbb{Z}_p$-homomorphism
As explained in the comments, if $B$ is $p$-complete (derived $p$-complete suffices), then the answer to 1- is yes.
This follows by adjunction from the fact that $A\to A\otimes_\mathbb Z \mathbb Z_p$ …
- 15.7k
14
votes
How to prove that topological Hochschild homology of a smooth proper stable k-linear infinit...
$\newcommand{\THH}{\mathrm{THH}}
\newcommand{\Cat}{\mathrm{Cat}}
\newcommand{\perf}{\mathrm{perf}}
\newcommand{\Sp}{\mathrm{Sp}}
\newcommand{\Mod}{\mathrm{Mod}}$
If you ask about dualizability in $\TH …
- 15.7k
7
votes
Accepted
Computing Ext groups in a functor stable $\infty$-category
$\newcommand{\Z}{\mathbb Z} \newcommand{\Ch}{\mathrm{Ch}} \newcommand{\Fun}{\mathrm{Fun}}$
Let $\Ch(\Z)$ be the projective model category of chain complexes. It is well known that it presents $D_\inft …
- 15.7k