Jonathan Gallagher

Date: March 9, 2018
Time: 12:00 am - 12:00 am
Location: ICT 616

Title: Frolicher spaces, Weil spaces, Diffeological spaces and abstract differential geometry
In differential geometry, obtaining a smooth structure on spaces of smooth maps is a motivation for the introduction of various kinds of generalized smooth spaces. Frechet manifolds do allow a manifold structure on the space of smooth maps between *finite* dimensional smooth manifolds, but the category is not cartesian closed. Frolicher spaces, Weil spaces, and diffeological spaces all have the advantage that they generalize smooth manifolds, and are cartesian closed categories.
We will describe these categories as Tangent categories. They are *not * tangent categories, but they should be. We will introduce a notion of generalized microlinearity, based on the work of Nishimura, whose notion was based on the work of Wraith and Kock, to extract a tangent full subcategory.