The effective model structure and infinity-groupoid objects
Journal article, 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

Author

Nicola Gambino

University of Leeds

Simon Henry

University of Ottawa

Christian Sattler

Chalmers, Computer Science and Engineering (Chalmers), Computing Science

Karol Szumilo

University of Warsaw

Forum of Mathematics, Sigma

20505094 (eISSN)

Vol. 10 e34

Proof theory and higher categorical semantics of homotopy type theory

Swedish Research Council (VR) (2019-03765), 2020-01-01 -- 2023-12-31.

Subject Categories

Algebra and Logic

Probability Theory and Statistics

Control Engineering

DOI

10.1017/fms.2022.13

More information

Latest update

1/3/2024 9