Two-dimensional category theory and Deligne's tensor product of abelian categories

Ignacio Lopez Franco (U Cambridge)

Wednesday 9th November, 2011 16:00-17:00 204


A tensor product of abelian categories, introduced by Deligne in his paper on Tannakian categories, has found applications on Hopf algebra theory and manifold invariants. However, very little has been studied about its properties and even its existence. In this talk I compare Deligne's tensor product with an older tensor product of categories with finite colimits by using several pieces of two-dimensional category theory, in particular 2-monads. It turns out that when the former tensor product exists (and not always does) it coincides with the latter.

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