Diagrammatic sets as a model of homotopy types
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917722076479488 |
|---|---|
| author | Chanavat, Clémence Hadzihasanovic, Amar |
| author_facet | Chanavat, Clémence Hadzihasanovic, Amar |
| contents | Diagrammatic sets are presheaves on a rich category of shapes, whose definition is motivated by combinatorial topology and higher-dimensional diagram rewriting. These shapes include representatives of oriented simplices, cubes, and positive opetopes, and are stable under operations including Gray products, joins, suspensions, and duals. We exhibit a cofibrantly generated model structure on diagrammatic sets, as well as two separate Quillen equivalences with the classical model structure on simplicial sets. We construct explicit sets of generating cofibrations and acyclic cofibrations, and prove that the model structure is monoidal with the Gray product of diagrammatic sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diagrammatic sets as a model of homotopy types Chanavat, Clémence Hadzihasanovic, Amar Algebraic Topology Category Theory 18N40, 18N50, 55P15, 55U05, 55U35 Diagrammatic sets are presheaves on a rich category of shapes, whose definition is motivated by combinatorial topology and higher-dimensional diagram rewriting. These shapes include representatives of oriented simplices, cubes, and positive opetopes, and are stable under operations including Gray products, joins, suspensions, and duals. We exhibit a cofibrantly generated model structure on diagrammatic sets, as well as two separate Quillen equivalences with the classical model structure on simplicial sets. We construct explicit sets of generating cofibrations and acyclic cofibrations, and prove that the model structure is monoidal with the Gray product of diagrammatic sets. |
| title | Diagrammatic sets as a model of homotopy types |
| topic | Algebraic Topology Category Theory 18N40, 18N50, 55P15, 55U05, 55U35 |
| url | https://arxiv.org/abs/2407.06285 |