On the Kelly monoidal structure of $Λ$-sequences and unital operads
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918335907627008 |
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| author | Fan, Aowen Zou, Foling |
| author_facet | Fan, Aowen Zou, Foling |
| contents | Let $Λ$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $Λ$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor from right modules in $Λ$-sequences to right modules in symmetric sequences is an isomorphism. We show that any compatible lower data extends to a normal oplax monoidal structure and use this to establish a universal normal oplax monoidal structure on $Λ$-sequences extending the Kelly product, identifying unital operads to monoids in unital $Λ$-sequences for a general symmetric monoidal category $\mathscr{V}$. We also establish a closed monoidal localization theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Kelly monoidal structure of $Λ$-sequences and unital operads Fan, Aowen Zou, Foling Algebraic Topology Category Theory Let $Λ$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $Λ$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor from right modules in $Λ$-sequences to right modules in symmetric sequences is an isomorphism. We show that any compatible lower data extends to a normal oplax monoidal structure and use this to establish a universal normal oplax monoidal structure on $Λ$-sequences extending the Kelly product, identifying unital operads to monoids in unital $Λ$-sequences for a general symmetric monoidal category $\mathscr{V}$. We also establish a closed monoidal localization theorem. |
| title | On the Kelly monoidal structure of $Λ$-sequences and unital operads |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2602.12738 |