Acyclic types and epimorphisms in homotopy type theory

Add to your list(s) Download to your calendar using vCal

• Tom de Jong (University of Nottingham)
• Friday 21 October 2022, 13:30-14:20
• LG23, SoCS and Zoom (see abstract for link).

If you have a question about this talk, please contact George Kaye.

Tom day Jong!

Zoom details

• Link: https://bham-ac-uk.zoom.us/j/81873335084?pwd=T1NaUFg2U1l6d0RLL2RlTzFBam1IUT09
• Meeting ID: 818 7333 5084
• Passcode: 217

Abstract

It is well known that the epimorphisms in the category of sets are exactly the surjections. But what are the epimorphisms of types? Thinking of types as spaces, and following literature in algebraic topology, we characterise epimorphisms of types in homotopy type theory (HoTT) as so-called acyclic maps. An acyclic map is a map whose fibres are acyclic types, and a type is acyclic if its suspension is contractible. We also consider a weaker notion called k-acyclicity (for k ≥ -2) and show for example that the classifying type of a group G is 2-acyclic if and only if the group G is perfect, i.e. its abelianisation is trivial. I will not assume any familiarity with HoTT and pause to introduce the relevant notions.

This is joint work with Ulrik Buchholtz and Egbert Rijke.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• LG23, SoCS and Zoom (see abstract for link)
• Theoretical computer science seminar
• computer sience

Note that ex-directory lists are not shown.