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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-2219-kr72 |
| Date | January 2020 |
| Creators | Kravets, Oleksandr |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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