Author: Eiko
Tags: category theory, morita equivalence, algebra
Time: 2024-11-11 00:23:57 - 2024-11-11 00:31:19 (UTC)
Morita Equivalence
Can be viewed as a baby version of derived equivalence, when we say two algebras and are Morita equivalence, they are equivalent in a deep sense. Precisely speaking it means their module categories are equivalent.
Full-idempotent Give Morita Equivalence
When you have a full idempotent in , i.e. an idempotent that satisfy , here the left side accepts linear extending. Then is automatically Morita equivalent to , the functor is given by
with reverse functor given by
Note that here is a right module because .