Title: Drazin Inverses in Categories
Abstract: In this talk, I will introduce Drazin inverses from a categorical perspective. Drazin inverses are a fundamental algebraic structure which have been extensively deployed in semigroup theory and ring theory. Drazin inverses can also be defined for endomorphisms in any category. In this talk, I will introduce Drazin categories, in which every endomorphism has a Drazin inverse, and provide various examples including the category of matrices over a field, and explore various properties of these inverses.
