Geodesic
Strictification of ∞-groupoids is comonadic
Theory and applications of categories, Tome 44 (2025), pp. 277-304.

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We investigate the universal strictification adjunction from weak infininity-groupoids (modeled as simplicial sets) to ``strict infinity-groupoids'', more commonly called ``omega-groupoids''. Modeling these with simplicial T-complexes, we prove that any simplicial set can be recovered up to weak homotopy equivalence as the totalization of its canonical cosimplicial resolution induced by this adjunction. We explain how this generalizes the fact due to Bousfield and Kan that the homotopy type of a simply connected space can be recovered as the totalization of its canonical cosimplicial resolution induced by the free simplicial abelian group adjunction. Furthermore, we leverage this result to show that this strictification adjunction induces a comonadic adjunction between the quasicategories of simplicial sets and omega-groupoids.
Publié le :
Classification : 18N30, 18N10, 55U10
Keywords: strictification, infinity-groupoid, omega-groupoid, comonadic 
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     author = {Kimball Strong},
     title = {Strictification of \ensuremath{\infty}-groupoids is comonadic},
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     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a8/}
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Kimball Strong. Strictification of ∞-groupoids is comonadic. Theory and applications of categories, Tome 44 (2025), pp. 277-304. http://geodesic.mathdoc.fr/item/TAC_2025_44_a8/