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SUMMARY:Uniform Kan fibrations from scratch - Eric Faber (DPMMS)
DTSTART:20180515T131500Z
DTEND:20180515T141500Z
UID:TALK105931@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:It has been known for some time that the standard theory of Ka
 n 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 weak factorization systems featuring 
 'uniform' Kan fibrations. In this talk I will show that it is possible to 
 arrive at uniform Kan fibrations from scratch using a path object due to G
 arner and Van den Berg and a new class of generating trivial cofibrations 
 called 'mould inclusions'. This approach avoids \nnon-constructive aspects
  of weak factorisation systems from the outset and focuses on Kan fibratio
 ns as modelling dependent types. This is joint work with Benno van den Ber
 g.
LOCATION:MR3\, Centre for Mathematical Sciences
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