The effective model structure and infinity-groupoid objects
Artikel i vetenskaplig tidskrift, 2022

For a category E with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in E, generalising the Kan-Quillen model structure on simplicial sets. We then prove that the effective model structure is left and right proper and satisfies descent in the sense of Rezk. As a consequence, we obtain that the associated infinity-category has finite limits, colimits satisfying descent, and is locally Cartesian closed when E is but is not a higher topos in general. We also characterise the infinity-category presented by the effective model structure, showing that it is the full sub-category of presheaves on E spanned by Kan complexes in E, a result that suggests a close analogy with the theory of exact completions.

Model structure

Författare

Nicola Gambino

University of Leeds

Simon Henry

University of Ottawa

Christian Sattler

Chalmers, Data- och informationsteknik, Computing Science

Karol Szumilo

Uniwersytet Warszawski

Forum of Mathematics, Sigma

20505094 (eISSN)

Vol. 10 e34

Bevisteori och semantik för homotopitypteori i högre ordningens kategorier

Vetenskapsrådet (VR) (2019-03765), 2020-01-01 -- 2023-12-31.

Ämneskategorier

Algebra och logik

Sannolikhetsteori och statistik

Reglerteknik

DOI

10.1017/fms.2022.13

Mer information

Senast uppdaterat

2024-01-03