Abstract David Yetter

Abstract:  There is a folk-theorem that generalizes Gerstenhaber's characterization of (infinitesimal) deformations of associative algebras in terms of Hochschild cohomology to deformations of k-linear categories (algebroids in the sense of Mitchell) in terms of an obvious generalized Hochschild cohomology.  In this talk I will discuss this, and its extension to a deformation theory for pasting diagrams of k-linear categories, k-linear functors, and natural transformations (with portions specified as commuting) using a slightly less obvious generalization of Hochschild cohomology and lots of mapping cones over chain maps, some obvious, some much less so, as well as reasons to care about such a deformation theory.

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