A criterion for existence of right-induced model structures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866912962412806144 |
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| author | Drummond-Cole, Gabriel C. Hackney, Philip |
| author_facet | Drummond-Cole, Gabriel C. Hackney, Philip |
| contents | Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when $F$ admits both adjoints. We give several examples, including change-of-rings, operad-like structures, and anti-involutive structures on infinity categories. For the last of these, we explore anti-involutive structures for several different models of $(\infty, 1)$-categories, and show that known Quillen equivalences between base model categories lift to equivalences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_07787 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A criterion for existence of right-induced model structures Drummond-Cole, Gabriel C. Hackney, Philip Category Theory Algebraic Topology Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when $F$ admits both adjoints. We give several examples, including change-of-rings, operad-like structures, and anti-involutive structures on infinity categories. For the last of these, we explore anti-involutive structures for several different models of $(\infty, 1)$-categories, and show that known Quillen equivalences between base model categories lift to equivalences. |
| title | A criterion for existence of right-induced model structures |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/1712.07787 |