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Cofibration category of digraphs for path homology
Carranza, Daniel1; Doherty, Brandon2; Kapulkin, Krzysztof3; Opie, Morgan4; Sarazola, Maru5; Wong, Liang Ze6
1 Johns Hopkins University Department of Mathematics 3400 N. Charles Street Baltimore MD 21218 (USA)
2 Florida State University Department of Mathematics 208 Love Building, 1017 Academic Way Tallahassee FL 32306 (USA)
3 University of Western Ontario Department of Mathematics 1151 Richmond Street London, Ont. N6A 5B7, Canada
4 University of California Los Angeles Department of Mathematics 520 Portola Plaza Los Angeles CA 90095 (USA)
5 University of Minnesota School of Mathematics 206 Church St SE Minneapolis MN 55455 (USA)
6 Institute of High Performance Computing (IHPC) Agency for Science, Technology and Research (A*STAR) 1 Fusionopolis Way, #16-16 Connexis Singapore 138632, Republic of Singapore
Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 475-514.

We prove that the category of directed graphs and graph maps carries a cofibration category structure in which the weak equivalences are the graph maps inducing isomorphisms on path homology.

Received:
Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/alco.341
Classification: 18N45, 55U35, 05C20, 18N40
Keywords: cofibration, cofibration category, category, directed graph, path homology

Carranza, Daniel 1; Doherty, Brandon 2; Kapulkin, Krzysztof 3; Opie, Morgan 4; Sarazola, Maru 5; Wong, Liang Ze 6

1 Johns Hopkins University Department of Mathematics 3400 N. Charles Street Baltimore MD 21218 (USA)
2 Florida State University Department of Mathematics 208 Love Building, 1017 Academic Way Tallahassee FL 32306 (USA)
3 University of Western Ontario Department of Mathematics 1151 Richmond Street London, Ont. N6A 5B7, Canada
4 University of California Los Angeles Department of Mathematics 520 Portola Plaza Los Angeles CA 90095 (USA)
5 University of Minnesota School of Mathematics 206 Church St SE Minneapolis MN 55455 (USA)
6 Institute of High Performance Computing (IHPC) Agency for Science, Technology and Research (A*STAR) 1 Fusionopolis Way, #16-16 Connexis Singapore 138632, Republic of Singapore
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Carranza, Daniel; Doherty, Brandon; Kapulkin, Krzysztof; Opie, Morgan; Sarazola, Maru; Wong, Liang Ze. Cofibration category of digraphs for path homology. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 475-514. doi : 10.5802/alco.341. https://alco.centre-mersenne.org/articles/10.5802/alco.341/

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