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Given a $\mathbb{C}$-linear category $\mathrm{C}$, let’s understand $\mathbf{HH}(\mathrm{C})$, the Hochschild homology of $\mathrm{C}$ as natural transformation. Then for any $A\in \mathbf{HH}(\mathrm{...

Sorry for repost from Math Stack Exchange: Let $\mathscr{C}_0$ be a small idempotent complete stable category tensored over some symmetric monoidal category $\mathcal{E}$. Its Ind-completion $\mathscr{...

$\newcommand{\Trans}{\mathrm{Trans}}\newcommand{\H}{\mathrm{H}}\newcommand{\HH}{\mathrm{HH}}\newcommand{\Hom}{\mathrm{Hom}}\newcommand{\Mod}{\mathrm{Mod}}$Recently I noticed that one may regard the co/...

Let $A,B$ be $k$-linear (possibly, dg-)categories, let $f,g:A\to B$ be two linear functors, and let $T:f\Rightarrow g$ be a natural isomorphism. If one denotes by $C_\bullet(A,A)$ the standard ...

A recent paper of Ben-Zvi and Nadler gives a general formalism for understanding "dimensions" in sheaf theories. Without getting too far into details, amongst other things, this formalism allows us ...

I'm looking for directions to the literature that might contain fairly explicit constructions that might be called (the algebra of functions on) the "derived mapping space" from a simplicial set to a ...