[Alta-Logic] Peripatetic seminar: Wed 20th October

[Robin Cockett]

Time: 11:00am, Wed, 20th October

Place; ICT616

Speaker: Geoff Crutwell

Title: Differential and tangent structure for restriction categories


Abstract:
In the past few weeks, we've seen two ideas: differential restriction
categories, which capture partial settings in which one can differentiate
maps, and the manifold completion of a restriction category, which allows
one to glue objects of a restriction category together.

I'll briefly review these two ideas, before getting to the main problem:
the manifold completion of a differential restriction category is not
again a differential restriction category.  Instead, I'll show that
objects in the manifold completion of a differential restriction category
have tangent bundles, a generalization of the usual tangent bundle notion
from differential geeometry.  This general construction shares a number of
properties with the usual tangent bundle, and we can axiomatize these
properties to find tangent structure in other settings.