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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: MSRI: Online/Virtual
Speaker(s) Martina Rovelli (Australian National University)
Description No Description
Video

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

Abstract/Media

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

H.264 Video 25048_28437_8356_Model_Structures_for__-Groupoids_and__-Categories_on_Cubical_sets_with_Faces__Degeneracies__Connections_and_Diagonals.mp4