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- W4367693823 abstract "We define the monoidal category $(Poly_E,y,triangleleft)$ of polynomials under composition in any category $E$ with finite limits, including both cartesian and vertical morphisms of polynomials, and generalize to this setting the Dirichlet tensor product of polynomials $otimes$, duoidality of $otimes$ and $triangleleft$, closure of $otimes$, and coclosures of $triangleleft$. We also prove that $triangleleft$-comonoids in $Poly_E$ are precisely the internal categories in $E$ whose source morphism is exponentiable, generalizing a result of Ahman-Uustalu equating categories with polynomial comonads, and show that coalgebras in this setting correspond to internal copresheaves. Finally, the double category of ``typed'' polynomials in $E$ is recovered using $triangleleft$-bicomodules in $Poly_E$." @default.
- W4367693823 created "2023-05-03" @default.
- W4367693823 creator A5014088772 @default.
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- W4367693823 date "2023-04-29" @default.
- W4367693823 modified "2023-09-26" @default.
- W4367693823 title "Structures on Categories of Polynomials" @default.
- W4367693823 doi "https://doi.org/10.48550/arxiv.2305.00167" @default.
- W4367693823 hasPublicationYear "2023" @default.
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