If $T$ is a triangulated category, then the formalism of $t$-structures gives a way to find abelian subcategories inside. You're supposed to find two strictly full subcategories, …

In the triangulated category $T$, say we have two distinguished triangles: $$X \xrightarrow{f} Y \rightarrow C_f \rightarrow X[1], $$ $$ X \xrightarrow{g} Y \rightarrow C_g \right …

Suppose we are given a thick subcategory of the compact objects in the homotopy category of modules over a ring spectrum $R$. Are there conditions we can place on $R$, or on the c …

Lurie's book, higher topos theory describes a new notion of a triangulated category, which is apparently much more natural than the usual definition. Obviously by now a great deal …

Two (finite-dimensional) $k$-algebras $A$ and $B$ are said to be stable equivalent if their stable module categories $\underline{\rm mod}(A)$ and $\underline{\rm mod}(B)$ are equiv …

I want to understand once and for all what the resolution of an unbounded complex is. I've been trying to read 'Homotopy limits in triangulated categories' by Marcel Bokstedt and A …

Is the stable homotopy category idempotent complete? I have not been able to prove it, and the proof for abelian groups seems to strongly rely on looking at elements. Thanks, Jon …

It is well known that non-uniqueness of a cone for a morphism in a triangulated category $C$ makes constructing exact functors (of triangulated categories) a difficult task. In sec …

I work in derived category $D^b(X)$ of constructible sheaves on a reasonable space $X$. Let $j\colon U\to X$ be an open inclusion and $i\colon Y\to X$ the closed complement. Let $M …

Given a stable quasicategory $C$, what are the conditions required of a subcategory for it to descend to a localizing subcategory in $Ho(C)$? Is it enough for it to be reflective? …

Set the framework to be a triangulated category with all set indexed coproducts. In "Relative Homological Algebra and Purity in Triangulated Categories", J. of Algebra 227, (2000) …

If $V$ is a monoidal model category, then its homotopy category $\mathrm{Ho}(V)$ is a monoidal category. Similarly, if $M$ is a $V$-model category, then $\mathrm{Ho}(M)$ is a $\ma …

Let $Q$ be a Dynkin quiver. Let $\mathbb CQ$ be its complex path algebra. It is defined in a way such that modules over $\mathbb CQ$ are the same as representations of the quiver $ …

The usual disclaimer applies: I'm new to all this stuff, so be gentle. It seems like the spectrum, as defined by Balmer, of the stable homotopy category of finite complexes is som …

Hello, I have terminological question. Consider the following properties of a full subcategory $B \subset A$, where $A$ is an abelian category, and we assume $B$ to be closed unde …