Home /  Cubical Sets (Part 2): Model structures for ∞-groupoids and ∞-categories on cubical sets with faces, degeneracies, connections and diagonals

Seminar

Cubical Sets (Part 2): Model structures for ∞-groupoids and ∞-categories on cubical sets with faces, degeneracies, connections and diagonals May 20, 2020 (02:00 PM PDT - 03:00 PM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Martina Rovelli (University of Massachusetts Amherst; Australian National University)
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Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Model Structures For ∞-Groupoids And ∞-Categories On Cubical Sets With Faces, Degeneracies, Connections And Diagonals
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Zoom Link:

https://msri.zoom.us/s/93059090699

 

When working with the (evil) category of cubes generated by faces, degeneracies, diagonals and connections, namely the full subcategory of Cat, we will show that one can use the triangulation functor to (both left- and right-)transfer the Kan model structure and the Joyal model structure from simplicial sets to cubical sets. The resulting model categories are Quillen equivalent to the Kan model structure and to the Joyal model structure, so they in particular model ∞-groupoids and ∞-categories, respectively.

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Model Structures For ∞-Groupoids And ∞-Categories On Cubical Sets With Faces, Degeneracies, Connections And Diagonals

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