Two remarks on spaces of maps between operads of little cubes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913968726999040 |
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| author | Horel, Geoffroy Krannich, Manuel Kupers, Alexander |
| author_facet | Horel, Geoffroy Krannich, Manuel Kupers, Alexander |
| contents | We record two facts on spaces of derived maps between the operads $E_d$ of little $d$-cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$ are automorphisms. We also discuss variants for localisations of $E_d$ and for versions with tangential structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00908 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Two remarks on spaces of maps between operads of little cubes Horel, Geoffroy Krannich, Manuel Kupers, Alexander Algebraic Topology Category Theory 18N70, 55P48, 55R80, 58D10 We record two facts on spaces of derived maps between the operads $E_d$ of little $d$-cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$ are automorphisms. We also discuss variants for localisations of $E_d$ and for versions with tangential structures. |
| title | Two remarks on spaces of maps between operads of little cubes |
| topic | Algebraic Topology Category Theory 18N70, 55P48, 55R80, 58D10 |
| url | https://arxiv.org/abs/2211.00908 |