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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.01625 |
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| _version_ | 1866913091618340864 |
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| author | Ko, Joanna |
| author_facet | Ko, Joanna |
| contents | Marked limits, or Cartesian quasi-limits introduced by Gray, give an alternative approach to $\mathbf{Cat}$-weighted limits in $2$-category theory. This was first established by Street, and we aim to give a new approach to this result using marked codescent objects of marked coherence data which we introduce in this article. We then propose the notion of dotted $2$-limits, which is a natural generalisation of marked limits to the enhanced $2$-categorical setting. We establish that dotted $2$-limits and $\mathscr{F}$-weighted limits both have the same expressive power. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01625 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dotted $2$-limits Ko, Joanna Category Theory 18N10 Marked limits, or Cartesian quasi-limits introduced by Gray, give an alternative approach to $\mathbf{Cat}$-weighted limits in $2$-category theory. This was first established by Street, and we aim to give a new approach to this result using marked codescent objects of marked coherence data which we introduce in this article. We then propose the notion of dotted $2$-limits, which is a natural generalisation of marked limits to the enhanced $2$-categorical setting. We establish that dotted $2$-limits and $\mathscr{F}$-weighted limits both have the same expressive power. |
| title | Dotted $2$-limits |
| topic | Category Theory 18N10 |
| url | https://arxiv.org/abs/2306.01625 |