3 papers
math.LO2023
Extensional concepts in intensional type theory, revisited
Chris Kapulkin, Yufeng Li
Revisiting a classic result from M. Hofmann's dissertation, we give a direct proof of Morita equivalence, in the sense of V. Isaev, between extensional type theory and intensional…
math.CO2023
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…
math.CO2023
The fundamental group in discrete homotopy theory
Chris Kapulkin, Udit Mavinkurve
We develop a robust foundation for studying the fundamental group(oid) in discrete homotopy theory, including: equivalent definitions and basic properties, the theory of covering g…