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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.

2 votes

Morita equivalence of DG algebras? (reference needed)

Just a comment on "For example, every linear invariant that I know of (algebraic K-theory, cyclic (co)homology, Hochschild (co)homology,...) is not only invariant under Morita equivalence but also und …
Marco Farinati's user avatar
2 votes

Morita equivalence of $K$-algebras

If V is a vector space such that $V\oplus V$ is isomorphic to V then A=TV, the tensor álgebra, is isomorphic to $T(V\oplus V)=A\coprod A$, in particular Morita equivalent
Marco Farinati's user avatar
1 vote

Morita equivalent algebras in a fusion category

in the algebra case, B=eMn(A)e "because" B=End_A (P) with P f.g. proyective, so, finding e is the same as give a presentation of P as a direct summand of A^n. Also, P=F(B) where F is the functor givin …
Marco Farinati's user avatar