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Cellular dg-categories and their applications to homotopy theory of A-infinity categories

Kravets, Oleksandr

We introduce the notion of cellular dg-categories mimicking the properties of topological CW-complexes. We study the properties of such categories and provide various examples corresponding to the well-known geometrical objects. We also show that these categories are suitable for encoding coherence conditions in homotopy theoretical constructs involving A-infinity categories. In particular, we formulate the notion of a homotopy coherent monoid action on an A-infinity category which can be used in constructions involved in Homological Mirror Symmetry.

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More About This Work

Academic Units
Mathematics
Thesis Advisors
Abouzaid, Mohammed
Degree
Ph.D., Columbia University
Published Here
June 17, 2020