Morita equivalence

Morita equivalence is a concept in category theory that describes when two categories are "essentially the same" from a categorical viewpoint. Specifically, two categories \( C \) and \( D \) are said to be Morita equivalent if they have equivalent categories of modules (or representations) in a way that preserves the structure of these categories. In more concrete terms, Morita equivalence can be understood in the context of ring theory.