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Algebra & Geometry Seminar

Speaker: Samuel Leblanc (Ñý¼§Ö±²¥)

Title: (Co)limit Computation and Its Application to Representation Theory

Abstract: A fundamental problem of representation theory is to classify functors C --> k-Vect up to isomorphism for a fixed small category C. Notable examples include when C = BG is a group, C = Q is a quiver, and C = P is a poset. Surprisingly, the limit and colimit of such functors provide some information about the decomposition of the functor into indecomposable summands. Motivated by this, in a joint work with T. Brüstle and J. Desrochers, we constructed the minimal full subcategory of a poset P that preserves the (co)limit of every functor P --> k-Vect. In this talk, we will explain these ideas, compute some examples, and discuss a possible generalization to arbitrary small categories.