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arXiv · 2306.02219

Nonexistence of colimits in naive discrete homotopy theory

Daniel Carranza·Chris Kapulkin·Jinho Kim
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Abstract

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 settle in the negative the question of whether the A-homotopy equivalences in the category of graphs are part of a model structure.

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Daniel Carranza, Chris Kapulkin, Jinho Kim. 2023-09-05. Nonexistence of colimits in naive discrete homotopy theory. https://arxiv.org/abs/2306.02219

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