Exponentials of non-singular simplicial sets

Vegard Fjellbo; John Rognes

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arXiv · 2001.09643

Exponentials of non-singular simplicial sets

Vegard Fjellbo·John Rognes

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Abstract

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.

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Vegard Fjellbo, John Rognes. 2020-01-27. Exponentials of non-singular simplicial sets. https://arxiv.org/abs/2001.09643

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