Discreteness and completeness for $Θ_n$-models of $(\infty,n)$-categories
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929690552303616 |
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| author | Bergner, Julia E. |
| author_facet | Bergner, Julia E. |
| contents | We establish cartesian model structures for variants of $Θ_n$-spaces in which we replace some or all of the completeness conditions by discreteness conditions. We prove that they are all equivalent to each other and to the $Θ_n$-space model, and we give a criterion for which combinations of discreteness and completeness give non-overlapping models. These models can be thought of as generalizations of Segal categories in the framework of $Θ_n$-diagrams. In the process, we give a characterization of the Dwyer-Kan equivalences in the $Θ_n$-space model, generalizing the one given by Rezk for complete Segal spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Discreteness and completeness for $Θ_n$-models of $(\infty,n)$-categories Bergner, Julia E. Algebraic Topology Category Theory We establish cartesian model structures for variants of $Θ_n$-spaces in which we replace some or all of the completeness conditions by discreteness conditions. We prove that they are all equivalent to each other and to the $Θ_n$-space model, and we give a criterion for which combinations of discreteness and completeness give non-overlapping models. These models can be thought of as generalizations of Segal categories in the framework of $Θ_n$-diagrams. In the process, we give a characterization of the Dwyer-Kan equivalences in the $Θ_n$-space model, generalizing the one given by Rezk for complete Segal spaces. |
| title | Discreteness and completeness for $Θ_n$-models of $(\infty,n)$-categories |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2209.08156 |