Geodesic
Exponentials of non-singular simplicial sets
Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 307-314.

Voir la notice de l'article provenant de la source International Press of Boston

A simplicial set is non-singular if the representing map of each non-degenerate simplex is degreewise injective. The simplicial mapping set $X^K$ has $n$‑simplices given by the simplicial maps $\Delta [n] \times K \to X$. We prove that $X^K$ is non-singular whenever $X$ is non-singular. It follows that non-singular simplicial sets form a cartesian closed category with all limits and colimits, but it is not a topos.
DOI : 10.4310/HHA.2022.v24.n2.a15
Classification : 18D15, 55U10
Keywords: non-singular simplicial set, exponential ideal, cartesian closed category 
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     title = {Exponentials of non-singular simplicial sets},
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     pages = {307--314},
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Vegard Fjellbo; John Rognes. Exponentials of non-singular simplicial sets. Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 307-314. doi : 10.4310/HHA.2022.v24.n2.a15. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a15/

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