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CATEGORIES:Category Theory Seminar
SUMMARY:Uniform Kan fibrations from scratch - Eric Faber (
DPMMS)
DTSTART;TZID=Europe/London:20180515T141500
DTEND;TZID=Europe/London:20180515T151500
UID:TALK105931AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/105931
DESCRIPTION:It has been known for some time that the standard
theory of Kan simplicial sets unavoidably uses non
-constructive axioms. In recent work\, Gambino and
Sattler have made progress towards a constructive
theory of Kan simplicial sets using algebraic wea
k factorization systems featuring 'uniform' Kan fi
brations. In this talk I will show that it is poss
ible to arrive at uniform Kan fibrations from scra
tch using a path object due to Garner and Van den
Berg and a new class of generating trivial cofibra
tions called 'mould inclusions'. This approach avo
ids \nnon-constructive aspects of weak factorisati
on systems from the outset and focuses on Kan fibr
ations as modelling dependent types. This is joint
work with Benno van den Berg.
LOCATION:MR3\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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