Definition and context: An (associative, unital, not necessarily commutative) ring $R$ is called classical if every regular element of $R$ is a unit. Equivalently, $R$ is its own …

Recall that algebras (or linear 1-categories) $A$ and $B$ are Morita equivalent if there exist bimodules $_AM_B$ and $_BN_A$ and isomorphisms $u: {}_A(M \otimes_BN)_A \to {}_AA_A$ …

Suppose I have a fusion category $\mathcal{C}$ and an indecomposable module category $\mathcal{M}$ over it. The commutant $\mathcal{C}_\mathcal{M}^*$ is the category of module endo …

I have often encountered definitions of the kind "stacks are equivalence classes of groupoids under Morita equivalence" in topological or differentiable context, with the notion of …

Let $K$ be a compact or a finite group with a closed subgroup $H$. Let $C(K)$ be the convolution algebra of continuous functions on $K$. The Peter Weyl theorem asserts that the $* …

Hi, I wonder if there is a name for: 1) Algebras which are Morita equivalent to their centers, or 2) dg-algebras which are derived Morita equivalent to their Hochshild cohomolog …

A stupid question: whether ther exists a universally recognized definition of when two differential graded algebras should be Morita equivalent? I mean a sort of equivalence which …

Lie groupoids are groupoids with smooth structures. There is a nature 2-category of Lie groupoids: Lie groupoids, smooth functors of Lie groupoids, smooth natural transformations o …

Given a projective scheme $X$, say over $\mathbb{C}$, another $\mathbb{C}$-scheme $S$ and a coherent and torsion free (as an $O_X$-module) $M_n(O_X)$-module $F$. Now we can use Mo …

Following the notation of Etingof-Nikshych-Ostrik what is Out(G-mod) for a finite group G? That is what are all bimodule cateogries over the fusion category G-mod of complex G-mod …

Associated to any $A_\infty$ $k$-algebra $A$ the Hochschild cochain complex $CH^*(A)$ has the structure of a dg-Lie algebra and a dg-algebra which are compatible enough that the co …