Luke Steverango (Queen's University)

Curves Seminar

Speaker: Luke Steverango (Queen's University)

Title: Locally Finite (Artinian) Categories and Co-Algebras

Abstract: In this talk we will define an important type of category: locally finite categories. Many of the categories we will be working with will be locally finite. After talking through details about locally finite and finite categories, we will turn our attention to co-algebras with the aim to eventually prove Theorem 1.9.15 due to Takeuchi: Any essentially small locally finite abelian category C over a field k is equivalent to the category C-comod for a unique pointed coalgebra C. In particular, if C is finite, it is equivalent to the category A-mod for a unique basic algebra A.