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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Funding
This material is based upon work supported by the National Science Foundation under Grant No. DMS-1928930 while the first two authors participated in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the 2022–23 academic year.
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All authors (DC, CK, and JK) contributed equally to the research and preparation of this work.
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Communicated by Tobias Dyckerhoff.
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Carranza, D., Kapulkin, K. & Kim, J. Nonexistence of Colimits in Naive Discrete Homotopy Theory. Appl Categor Struct 31, 41 (2023). https://doi.org/10.1007/s10485-023-09746-9
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DOI: https://doi.org/10.1007/s10485-023-09746-9