2-stacks over bisites
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917611894210560 |
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| author | Caviglia, Elena |
| author_facet | Caviglia, Elena |
| contents | We generalize the concept of stack one dimension higher, introducing a notion of 2-stack suitable for a trihomomorphism from a 2-category equipped with a bitopology into the tricategory of bicategories. Moreover, we give a characterization of 2-stacks in terms of explicit conditions, that are easier to use in practice. These explicit conditions are effectiveness conditions for appropriate data of descent on objects, morphisms and 2-cells, generalizing the usual stacky gluing conditions one dimension higher. Furthermore, we prove some new results on bitopologies. The main one is that every object of a subcanonical bisite can be seen as the sigma-bicolimit of each covering bisieve over it. This generalizes one dimension higher a well-know result for subcanonical Grothendieck sites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2-stacks over bisites Caviglia, Elena Category Theory Algebraic Geometry 18F20, 18F10, 18N20, 18N10 We generalize the concept of stack one dimension higher, introducing a notion of 2-stack suitable for a trihomomorphism from a 2-category equipped with a bitopology into the tricategory of bicategories. Moreover, we give a characterization of 2-stacks in terms of explicit conditions, that are easier to use in practice. These explicit conditions are effectiveness conditions for appropriate data of descent on objects, morphisms and 2-cells, generalizing the usual stacky gluing conditions one dimension higher. Furthermore, we prove some new results on bitopologies. The main one is that every object of a subcanonical bisite can be seen as the sigma-bicolimit of each covering bisieve over it. This generalizes one dimension higher a well-know result for subcanonical Grothendieck sites. |
| title | 2-stacks over bisites |
| topic | Category Theory Algebraic Geometry 18F20, 18F10, 18N20, 18N10 |
| url | https://arxiv.org/abs/2403.08030 |