The fibration sequences of the lattice path operad
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913745058398208 |
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| author | De Leger, Florian |
| author_facet | De Leger, Florian |
| contents | We introduce a notion of an operad of complexity $m$, for $m \geq 1$. Operads of complexity $1$ are monoids in the category of $\mathbb{N}$-indexed collections, with monoidal product given by the Day convolution, and operads of complexity $2$ are non-symmetric operads. In general, we prove that the operad for operads of complexity $m$ is a suboperad of the $m$-th stage filtration of the lattice path operad introduced by Batanin and Berger. Finally, we exhibit fibration sequences involving this new notion, extending the results of Turchin and Dwyer-Hess. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The fibration sequences of the lattice path operad De Leger, Florian Algebraic Topology We introduce a notion of an operad of complexity $m$, for $m \geq 1$. Operads of complexity $1$ are monoids in the category of $\mathbb{N}$-indexed collections, with monoidal product given by the Day convolution, and operads of complexity $2$ are non-symmetric operads. In general, we prove that the operad for operads of complexity $m$ is a suboperad of the $m$-th stage filtration of the lattice path operad introduced by Batanin and Berger. Finally, we exhibit fibration sequences involving this new notion, extending the results of Turchin and Dwyer-Hess. |
| title | The fibration sequences of the lattice path operad |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2503.15179 |