[Alta-Logic] Peripatetic Seminar for 2025 April 25

[Kristine Bauer]

HI everyone,

I would like to invite you to join me tomorrow at the Topos Institute virtual seminar.  I am giving the talk - title/abstract below.  To save you the trouble of converting time zones, the talk is at 11:00 am.

In case you are planning to attend FMCS this year, I will be giving a version of this talk at FMCS delivered as a tutorial (slower and with more background!!).

Cheers,
Kristine



From: Tim Hosgood <tim at topos.institute<mailto:tim at topos.institute>>
Subject: Topos Institute Colloquium (1st of May)
Date: 28 April 2025 at 17:37:54 CEST
To: Seminars at Topos Institute <seminars at topos.institute<mailto:seminars at topos.institute>>
Reply-To: tim at topos.institute<mailto:tim at topos.institute>

Hi everyone,

Below is the title and abstract for the next talk at the Topos Institute Colloquium, this Thursday at 17:00 UTC. You can check what time this is in your local time zone on either the website<https://topos.institute/events/topos-colloquium/> or ResearchSeminars page<https://researchseminars.org/seminar/ToposInstituteColloquium>. Everybody is welcome to attend, either via Zoom or by the YouTube live stream.

More information can be found at https://topos.institute/events/topos-colloquium.

Looking forward to seeing you all there!

Best, Tim

——————

Talk details

Kristine Bauer: Distillation systems as models of homotopy colimits

This is joint work with Kathryn Hess, Brenda Johnson and Julie Rasmusen.

Colimits (and limits) are among the most fundamental notions in category theory, and also among the most useful of the basic structures. In topology, colimits are used to “glue” spaces together. However, problems arise when we try to work with spaces as they continuously deform, because colimits are not invariant under such deformations. In this case, one uses a related notion called a homotopy colimit. But what are these, really? Homotopy colimits do not satisfy a universal property, even in the homotopy category, and are usually defined by the way they are computed in particular types of categories, such as model categories. In joint work, Hess and Johnson identified a list of properties that one would expect homotopy limits to satisfy in any homotopical category. These properties were chosen carefully because they are needed to perform certain constructions in functor calculus. Building on their work, we have identified the categorical structures that govern these properties. A distillation system relates two actions of the category of small categories on the category of categories through a lax linear functor. In this talk, I will define distillation systems and explain when they do and don’t recover homotopy colimits.

Zoom: https://topos-institute.zoom.us/j/84392523736?pwd=bjdVS09wZXVscjQ0QUhTdGhvZ3pUdz09
YouTube: youtube.com/live/L4drX4HbySY<https://www.youtube.com/live/L4drX4HbySY>

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