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CATEGORIES:Category Theory Seminar
SUMMARY:Homotopy type theory and algebraic weak factorizat
ion systems - Nicola Gambino (University of Leeds)
DTSTART;TZID=Europe/London:20170131T141500
DTEND;TZID=Europe/London:20170131T151500
UID:TALK70601AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/70601
DESCRIPTION:The theory of weak factorisation systems and Quill
en model structures provides a very convenient set
ting to construct and analyze models of Homotopy T
ype Theory\, most notably the simplicial model def
ined by Voevodsky\, in which types are interpreted
as Kan fibrations.\n\nThe aim of this talk is to
explain how the theory of algebraic weak factoriza
tion systems provides an analogous understanding o
f the cubical model of Homotopy Type Theory define
d by Coquand and his collaborators\, in which type
s are interpreted as uniform Kan fibrations\, i.e.
fibrations equipped with a suitably coherent choi
ce of diagonal fillers. This involves the develop
ment of a general method to construct algebraic wh
ich satisfy the so-called Frobenius property\, and
leads to a new proof of the right properness of t
he model structure for Kan complexes.\n\nThe talk
is based on joint work with Christian Sattler (Lee
ds).\n
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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