The tag has no usage guidance.

learn more… | top users | synonyms

3
votes
0answers
84 views

Short proof of the classification of representation-finite symmetric algebras up to stable equivalence

Assume $K$ is an algebraically closed field and $A$ a finite dimensional $K$-algebra. Assume additionally that $A$ is symmetric and representation-finite. Then one has the following classification of ...
8
votes
2answers
274 views

derived categories as presentable DG-categories

Let $A$ be a ring. Is it true that the DG category of unbounded complexes of $A$-modules, localized by quasi-isomorphisms, is cocomplete and compactly generated? What would be a reference for that and ...
-1
votes
1answer
388 views

$E_n$ structures on Symmetric Monoidal Stable infinity-categories [closed]

Let $C$ be a stable $∞$-category with a monoidal structure on it, hence a monoidal stable $∞$-category; if this monoidal structure is "maximally symmetric" (in Wikipedia's sense) $C$ is a symmetric ...
4
votes
0answers
139 views

Stable $\infty$ categories as a 2-category

Is there a treatment in the literature of stable $\infty$ categories as a 2-category? I.e. with non invertible 2-morphisms. Mostly I am interested in the behavior of the tensor product with respect ...
6
votes
1answer
280 views

When was the word “stable” first used to describe stable homotopy theory?

The word "stable" has many uses in mathematics, but in the context of stable homotopy theory, one might take it to mean one of two things: Homotopy groups stabilize after taking suspensions (...
3
votes
1answer
272 views

Does Ind-completion commute with finite limits?

The broad and vague question is in the title. The more precise question is: Say $\{\mathcal{C}_i\}$ is a finite diagram of (essentially small) stable $\infty$-categories and exact functors with ...
13
votes
3answers
1k views

how to make the category of chain complexes into an $\infty$-category

I'd like to have some simple examples of quasi-categories to understand better some concepts and one of the most basic (for me) should be the category of chain complexes. Has anyone ever written down ...
8
votes
1answer
376 views

Heller operator without left adjoint?

Suppose given a noetherian ring $R$. On the stable category $R\text{-}\underline{\text{mod}} := R\text{-mod}/R\text{-proj}$, we have the Heller operator $$ \Omega : R\text{-}\underline{\text{mod}} \...