3 citations · 5 across the 13 of their papers we have counts for
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Nonexistence of colimits in naive discrete homotopy theory
Daniel Carranza, Chris Kapulkin, Jinho Kim
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 set…
Calculus of Fractions for Quasicategories
Daniel Carranza, Chris Kapulkin, Zachery Lindsey
We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove…
Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories
Daniel Carranza, Chris Kapulkin, Liang Ze Wong
The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal…