A Cartesian Promonoidal Kernel on $Δ$ and a Hadamard Contraction of $Δ^n$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908619645124608 |
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| author | Lengyel, Florian |
| author_facet | Lengyel, Florian |
| contents | We exhibit a symmetric promonoidal kernel on the simplex category $Δ$ with Cartesian unit, yielding on representable functors a Hadamard natural transformation $Δ^p\timesΔ^q\toΔ^{pq}$ based on pointwise multiplication of nondecreasing maps. Specializing to $q=1$ yields a simplicial homotopy contracting $Δ^n$ to its $0$-vertex. The contraction is classical; the promonoidal presentation and induced Hadamard map appear not to be recorded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19104 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Cartesian Promonoidal Kernel on $Δ$ and a Hadamard Contraction of $Δ^n$ Lengyel, Florian Category Theory Algebraic Topology 18D10, 18M15, 18A40, 55U10 We exhibit a symmetric promonoidal kernel on the simplex category $Δ$ with Cartesian unit, yielding on representable functors a Hadamard natural transformation $Δ^p\timesΔ^q\toΔ^{pq}$ based on pointwise multiplication of nondecreasing maps. Specializing to $q=1$ yields a simplicial homotopy contracting $Δ^n$ to its $0$-vertex. The contraction is classical; the promonoidal presentation and induced Hadamard map appear not to be recorded. |
| title | A Cartesian Promonoidal Kernel on $Δ$ and a Hadamard Contraction of $Δ^n$ |
| topic | Category Theory Algebraic Topology 18D10, 18M15, 18A40, 55U10 |
| url | https://arxiv.org/abs/2510.19104 |