March 14 (! now on DAYLIGHT TIME !): Greta Coraglia "On the fibration of algebras"

[Emily Riehl]

The HoTTEST seminar continues this week, on Thursday (π-day), at the BRAND NEW SUMMER TIME: 11:30am EDT = 15:30 UTC. For those of you who have not recently gone through the daylight savings time switch, this means that the seminar will be one hour earlier than usual.

Our speaker is Greta Coraglia, whose talk is titled "On the fibration of algebras".  The talk will be 60 minutes long, followed by
up to 30 minutes for questions.  The abstract is below.

The Zoom link is https://zoom.us/j/994874377

Further information, including the list of upcoming speakers, and videos and slides from past talks, is at:

 

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

Emily

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

 

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Title: On the fibration of algebras

Abstract: We study fibrations arising from indexed categories of the following form: for a parametric endofunctor, consider its category of algebras (or Kleisli/Eilenberg--Moore in the case of monads), then one can construct the (op)fibration having for base category that of parameters, so that each fiber is precisely the category of algebras on a given fixed parameter. Examples of such constructions arise in disparate areas of mathematics, and are unified by the intuition that the resulting total category is a form of "semidirect product" of the category of parameters, which acts on the category the parametric endofunctor is defined on. We discuss some properties and applications with respect to the categorical semantics of (co)induction.

This is part of a joint and ongoing work with D. Ahman, D. Castelnovo, F. Loregian, N. Martins-Ferreira, Ü. Reimaa.

 

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Professor of Mathematics (she/her)
Johns Hopkins University
emilyriehl.github.io