19 citations · 22 across the 4 of their papers we have counts for
6 papers
Synthetic approach to the Quillen model structure on topological spaces
Sterling Ebel, Chris Kapulkin
We provide an axiomatic treatment of Quillen's construction of the model structure on topological spaces to make it applicable to a wider range of settings, including -generated…
Closed symmetric monoidal structures on the category of graphs
Chris Kapulkin, Nathan Kershaw
We show that the category of (reflexive) graphs and graph maps carries exactly two closed symmetric monoidal products: the box product and the categorical product.
Homotopical inverse diagrams in categories with attributes
Chris Kapulkin, Peter LeFanu Lumsdaine
We define and develop the infrastructure of homotopical inverse diagrams in categories with attributes. Specifically, given a category with attributes and an ordered homotopica…
The homotopy theory of type theories
Chris Kapulkin, Peter LeFanu Lumsdaine
We construct a left semi-model structure on the category of intensional type theories (precisely, on ). This presents an -category of su…
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.
Homotopy Theoretic Models of Type Theory
Peter Arndt, Chris Kapulkin
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that o…