Sept 6: Reid Barton,

[Dan Christensen]

The HoTTEST seminar begins its fall season with the following talk:

Reid Barton

Directed aspects of condensed type theory

The talk is at 11:30am EDT (15:30 UTC) on Thursday, September 26. The
talk will be 60 minutes long, followed by up to 30 minutes for
questions. See

https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html

for the Zoom link, the abstract, and a list of all upcoming talks.

All are welcome!

Abstract:

Condensed mathematics is a recently-introduced setting for applying
methods of higher category theory to objects of topological nature.
The category Cond of condensed sets can be viewed as an approximation
of the category of topological spaces by a topos. We identify two
classes of maps of Cond, that we call "etale" and "proper", that
correspond to local homeomorphisms and to proper maps of topological
spaces respectively, and we propose type-theoretic axioms concerning
these that express the sense in which Cond is a "category of spaces",
and not only a "category of sets".

The focus of this talk will be on the "directed path types" of a
condensed set (or groupoid), which correspond to the specialization
order on the points of a topological space, and are defined using the
Sierpinski condensed set as "directed interval". Etale and proper maps
have unique lifting properties with respect to the two endpoints of
this interval, and so are analogous to left and right fibrations of
simplicial spaces. The aim of the talk is to explain this (imperfect)
analogy from both an external and an internal perspective, to try to
shed light on possible relationships with recent and current work in
simplicial and directed type theories.

This talk is based on joint work with Johan Commelin.

Dan

(On behalf of the HoTTEST organizers: Carlo Angiuli, Dan Christensen, Chris
Kapulkin, and Emily Riehl.)

[Dan Christensen]

I have corrected the subject line: Reid is speaking tomorrow, not three
weeks ago!

Dan