11 citations · 25 across the 6 of their papers we have counts for
6 papers
The effective model structure and -groupoid objects
Nicola Gambino, Simon Henry, Christian Sattler +1
For a category with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simpl…
The constructive Kan-Quillen model structure: two new proofs
Nicola Gambino, Christian Sattler, Karol Szumiło
We present two new proofs of Simon Henry's result that the category of simplicial sets admits a constructive counterpart of the classical Kan-Quillen model structure. Our proofs ar…
Internal Languages of Finitely Complete -categories
Chris Kapulkin, Karol Szumiło
We prove that the homotopy theory of Joyal's tribes is equivalent to that of fibration categories. As a consequence, we deduce a variant of the conjecture asserting that Martin-Löf…
Localization of Cofibration Categories and Groupoid -algebras
Markus Land, Thomas Nikolaus, Karol Szumiło
We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an applica…
Quasicategories of Frames of Cofibration Categories
Chris Kapulkin, Karol Szumiło
We show that the quasicategory of frames of a cofibration category, introduced by the second-named author, is equivalent to its simplicial localization.
Two Models for the Homotopy Theory of Cocomplete Homotopy Theories
Karol Szumiło
We prove that the homotopy theory of cofibration categories is equivalent to the homotopy theory of cocomplete quasicategories. This is achieved by presenting both homotopy theorie…