Enhancement for categories and homotopical algebra
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918349855784960 |
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| author | Kaledin, D. |
| author_facet | Kaledin, D. |
| contents | We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhancement for categories and homotopical algebra Kaledin, D. Algebraic Geometry Algebraic Topology Category Theory Representation Theory We develop foundations for abstract homotopy theory based on Grothendieck's idea of a "derivator". The theory is model-independent, and does not depend on model categories, nor on simplicial sets. It is designed to accomodate all the usual potential applications, such as e.g. enhancements for derived categories of coherent sheaves, in a way that is as close as possible to usual category theory. |
| title | Enhancement for categories and homotopical algebra |
| topic | Algebraic Geometry Algebraic Topology Category Theory Representation Theory |
| url | https://arxiv.org/abs/2409.17489 |