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Session S27 - Categories and Topology

Thursday, July 15, 11:30 ~ 12:00 UTC-3

Towards cotangent categories

Geoff Cruttwell

Mount Allison University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Tangent categories, first defined by Rosicky (and further developed in a series of recent papers) are a minimal setting for differential geometry (as opposed to synthetic differential geometry, which aims to be a "nicest" setting for differential geometry). They involve a category with an endofunctor on it which behaves like the tangent bundle. Many ideas and results from differential geometry have been generalized to tangent categories, including vector bundles, connections, and differential forms.

In this talk I'll discuss recent progress J.-S. Lemay and I have made towards defining and working with cotangent bundles in the setting of tangent categories. We'll also consider how one could define cotangent categories - a separate axiomatic structure consisting of a category equipped with an abstract cotangent bundle.

Joint work with J.-S. Lemay (Mount Allison University).

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