Unital k-Restricted Infinity-Operads
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909590590849024 |
|---|---|
| author | Dubey, Amartya Shekhar Liu, Yu Leon |
| author_facet | Dubey, Amartya Shekhar Liu, Yu Leon |
| contents | We study unital $\infty$-operads by their arity restrictions. Given $k \geq 1$, we develop a model for unital $k$-restricted $\infty$-operads, which are variants of $\infty$-operads which has only $(\leq k)$-arity morphisms, as complete Segal presheaves on closed $k$-dendroidal trees, which are closed trees build from corollas with valences $\leq k$. Furthermore, we prove that the restriction functors from unital $\infty$-operads to unital $k$-restricted $\infty$-operads admit fully faithful left and right adjoints by showing that the left and right Kan extensions preserve complete Segal objects. Varying $k$, the left and right adjoints give a filtration and a co-filtration for any unital $\infty$-operads by $k$-restricted $\infty$-operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17444 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unital k-Restricted Infinity-Operads Dubey, Amartya Shekhar Liu, Yu Leon Algebraic Topology Category Theory We study unital $\infty$-operads by their arity restrictions. Given $k \geq 1$, we develop a model for unital $k$-restricted $\infty$-operads, which are variants of $\infty$-operads which has only $(\leq k)$-arity morphisms, as complete Segal presheaves on closed $k$-dendroidal trees, which are closed trees build from corollas with valences $\leq k$. Furthermore, we prove that the restriction functors from unital $\infty$-operads to unital $k$-restricted $\infty$-operads admit fully faithful left and right adjoints by showing that the left and right Kan extensions preserve complete Segal objects. Varying $k$, the left and right adjoints give a filtration and a co-filtration for any unital $\infty$-operads by $k$-restricted $\infty$-operads. |
| title | Unital k-Restricted Infinity-Operads |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2407.17444 |