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Geometry-Topology Seminar

Thursday, March 23, 2023 - 5:15pm

Julian Holstein

Uni - Hamburg


University of Pennsylvania


This meeting of our seminar will be run in hybrid style, with the speaker and some members of our audience present in DRL 4C8, and others online via Zoom. To get the Zoom link, please e-mail

The algebraic analogue of the loop space construction of topological spaces is Adams’ cobar construction, it induces a Koszul duality between algebras and coalgebras, providing an equivalence of suitable homotopy theories of augmented differential graded algebras and differential graded conilpotent coalgebras.
I will talk about far-reaching generalisation of this result to categorical Koszul duality, introducing a category of coalgebras Quillen equivalent to differential graded categories.
This equivalence is moreover quasi-monoidal and by constructing internal homs of certain coalgebras we can construct a concrete closed monoidal model for dg categories. In particular this gives natural descriptions of mapping spaces and internal homs between dg categories.
This is joint work with A. Lazarev.