Two rings are said to be Morita equivalent if their categories of (left) modules are equivalent. The notion is also used in more general contexts when certain categories of representations are equivalent.

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Quick question about conjugate equivalence bimodules and inner products

let $A$ and $B$ be $W^{*}$-algebras, let $X$ be an $A-B$-equivalence bimodule (according to the definition given in "Morita equivalence for $C^*$-algebras and $W^*$-algebras" by Rieffel, ...
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In what generality does Eilenberg-Watts hold?

In homological algebra, the Eilenberg-Watts theorem states that if $F\colon\text{Mod}_R\to\text{Mod}_S$ is a right-exact coproduct preserving functor of modules, then $F\cong-\otimes_R F(R).$ The ...
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Which endomorphism algebras are not Morita-trivial?

Let $\mathcal C$ be a symmetric monoidal category — for example, $\mathcal C$ might be the category of $R$-modules for a commutative ring $R$. At a minimum, I request further that: $\mathcal C$ is ...
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Strong morita equivalence and morphims between $C^*-$algebras

Let $A$ and $B$ be two $C^*-$algebras, they are $strong$ $morita$ $equivalent$ if there exist a $(B,A)-$bimodule $E$, an $(A,B)-$bimodule $F$, such that $E\otimes_A F\cong B$, $F\otimes_B E\cong A$ ...
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Morita equivalence for operator algebras and tensor products, question about proof

This is a bit of a dumb question I know, but I was reading "Morita equivalence for C*-algebras and W*-algebras" by Rieffel, in this section about Morita equivalences and how they relate to forming ...
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For a ring $A$, is $A$ Morita equivalent to $M_\infty(A)$? [closed]

Let $A$ be a ring, let $M_n(A)$ be the ring of $n$-by-$n$ matrices with elements in $A$, $A$ is Morita equivalent to $M_n(A)$, I was wondering if this also applied to infinite matrices? That is, if ...
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Is “being a full ring of quotients” a Morita invariant property?

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 classical ring of ...
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Morita semi-equivalences

Recall that algebras (or linear 1-categories) $A$ and $B$ are Morita equivalent if there exist bimodules $_AM_B$ and $_BN_A$ and isomorphisms $u: {}_A(M \otimes_BN)_A \to {}_AA_A$ and $v: {}_B(N ...
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Are there better upper bounds on the rank of the commutant of a fusion module than the global dimension?

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 endofunctors, and gives ...
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Algebras Morita equivalent to their centers

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 cohomology? For instance, ...
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Morita equivalence for compact groups

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 $*$ algebra $C(K)$ and ...
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Morita equivalence of DG algebras? (reference needed)

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 would incorporate ...
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Compare three 2-categories of (Lie) groupoids

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 of smooth functors. ...
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Behaviour of Morita equivalence in families of sheaves

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 Morita equivalence to ...
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stacks as Morita equivalence classes

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 Morita equivalence ...
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What is Out(G-mod) for a finite group G?

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-modules which have the ...
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Regarding the Gerstenhaber bracket on Hochschild cohomology and Morita equivalence

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 cohomology is a ...