Inner autoequivalences in general and those of monoidal categories in particular
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913361866784768 |
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| author | Hofstra, Pieter Karvonen, Martti |
| author_facet | Hofstra, Pieter Karvonen, Martti |
| contents | We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence of binary coproducts, unifying various known one-dimensional results and providing tractable computational tools in the two-dimensional setting. In particular, we show that the isotropy 2-group of a monoidal category coincides with its Picard 2-group, i.e., the 2-group on its weakly invertible objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_03683 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inner autoequivalences in general and those of monoidal categories in particular Hofstra, Pieter Karvonen, Martti Category Theory 18G45, 18M05, 18N10 We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence of binary coproducts, unifying various known one-dimensional results and providing tractable computational tools in the two-dimensional setting. In particular, we show that the isotropy 2-group of a monoidal category coincides with its Picard 2-group, i.e., the 2-group on its weakly invertible objects. |
| title | Inner autoequivalences in general and those of monoidal categories in particular |
| topic | Category Theory 18G45, 18M05, 18N10 |
| url | https://arxiv.org/abs/2205.03683 |