Arrow Categories of Monoidal Model Categories
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2017
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911885130989568 |
|---|---|
| author | White, David Yau, Donald |
| author_facet | White, David Yau, Donald |
| contents | We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, and has the important consequence that it allows for the consideration of a monoidal product in cubical homotopy theory. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, topological spaces, and pro-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1703_05359 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Arrow Categories of Monoidal Model Categories White, David Yau, Donald Algebraic Topology Algebraic Geometry Category Theory K-Theory and Homology We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, and has the important consequence that it allows for the consideration of a monoidal product in cubical homotopy theory. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, topological spaces, and pro-categories. |
| title | Arrow Categories of Monoidal Model Categories |
| topic | Algebraic Topology Algebraic Geometry Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/1703.05359 |