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University of Cambridge > Talks.cam > Category Theory Seminar > The classifying weak omega-category of a type theory

## The classifying weak omega-category of a type theoryAdd to your list(s) Download to your calendar using vCal - Chris Kapulkin, University of Warsaw
- Tuesday 24 November 2009, 14:15-15:45
- MR9, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Julia Goedecke. Starting with [HS98] it has become clear that (weak) higher categories provide natural semantics for intensional Martin-Löf Type Theory. Roughly speaking, the semantics can be deﬁned by interpreting types as objects and terms as morphisms. The higher cells are given by identity types: a term ρ : Id(t,t′) is interpreted as a 2-cell [[ρ]] : [[t]] ⇒ [[t′ ]] and a term χ : Id(ρ,ρ′) as an appropriate 3-cell and so on. In my talk I would like to present the results by Lumsdaine [Lum08] and Garner and van den Berg [GvdB08], where they proved that with the interpretation as above every type carries a weak ω-category structure. Finally, I want to sketch a proposal for the construction of the classifying weak ω-category for a type theory according to [AKL09]. This is joint work with Steve Awodey and Peter LeFanu Lumsdaine (Carnegie Mellon University).
[AKL09] Steve Awodey, Chris Kapulkin, and Peter LeFanu Lumsdaine, [GvdB08] Richard Garner and Benno van den Berg, [HS98] Martin Hofmann and Thomas Streicher, [Lum08] Peter LeFanu Lumsdaine, This talk is part of the Category Theory Seminar series. ## This talk is included in these lists:- All CMS events
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