We construct a left semi-model structure on the category of intensional type theories
(precisely, on CxlCat Id, 1, Σ (, Π ext)). This presents an∞-category of such type theories; we …

Our goal in this paper is to prove an equivalence between the model categorical approach
to pro-categories, as studied by Isaksen, Schlank and the first author, and the∞–categorical …

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 …

We introduce the notion of a “category with path objects”, as a slight strengthening of
Kenneth Brown's classical notion of a “category of fibrant objects”. We develop the basic …

arXiv:1507.02648v2 [math.CT] 17 Sep 2017 Page 1 arXiv:1507.02648v2 [math.CT] 17 Sep 2017
LOCALLY CARTESIAN CLOSED QUASICATEGORIES FROM TYPE THEORY KRZYSZTOF …

We define and study homotopy groups of cubical sets. To this end, we give four definitions of
homotopy groups of a cubical set, prove that they are equivalent, and further that they agree …

We construct a category of fibrant objects C< P> in the sense of K. Brown from any indexed
frame (a kind of indexed poset generalizing triposes) P, and show that its homotopy category …

We show that the quasicategory defined as the localization of the category of (simple)
graphs at the class of A-homotopy equivalences does not admit colimits. In particular, we …

arXiv:2212.12568v1 [math.CO] 23 Dec 2022 Page 1 arXiv:2212.12568v1 [math.CO] 23 Dec
2022 Cofibration category of digraphs for path homology Daniel Carranza Brandon Doherty …

HOMOTOPY THEORY OF COFIBRATION CATEGORIES Introduction Page 1 Homology,
Homotopy and Applications, vol.18(2), 2016, pp.345–357 HOMOTOPY THEORY OF …