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Cubical Sets (Part 2): Homotopy coherent nerve and straightening, cubically May 11, 2020 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Online/Virtual
Speaker(s) Chris Kapulkin (University of Western Ontario)
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The main focus of this 2-part special is to show how two important constructions of higher category theory, namely the homotopy coherent nerve and the (un)straightening adjunction, are most naturally seen as cubical-to-simplicial. To this end, I will define the homotopy coherent nerve functor to be taking a *cubical* category to a simplicial set and will rephrase the (un)straightening adjunction accordingly. I will then show that the straightening-over-the-point functor is a co-reflective embedding of the category of simplicial sets into the category of cubical sets.

This talk is based on:

K, Voevodsky, "A cubical approach to straightening", preprint, 2018.

K, Lindsey, Wong, "A co-reflection of cubical sets into simplicial

sets with applications to model structures", New York Journal of

Mathematics 25 (2019).

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