[Alta-Logic] peripatetic seminar Wednesday

[Jonathan Gallagher]

Location: ICT 616 at 12:30 pm

Speaker: Geoff Cruttwell

Title: Differential forms in tangent categories

Abstract:
Tangent categories, first defined by Rosicky in 1984, have recently enjoyed
renewed interest in the category theory community.  A tangent category is a
category equipped with an abstract analog of the tangent bundle functor T
for smooth manifolds.  Examples include the category of smooth manifolds
and extensions of it (eg., convenient manifolds, synthetic differential
geometry), categories in algebraic geometry, and categorical models of
differential linear logic.

In this talk we will look at the question of how to define differential
forms in a tangent category.  It turns out that the most natural
formulation of differential forms in this setting is not the standard one
(in which a differential form of an object M is a map whose domain is the
object of n tangent vectors at a point of M) but instead are maps whose
domain is the result of n applications of T to M.  We'll look at the
definition of these "singular" forms, a closely related notion of "tangent
form", and discuss how these two definitions relate to classical
differential forms.

This is joint work with Rory Lucyshyn-Wright.
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