论文标题
非单明简单组的指数
Exponentials of non-singular simplicial sets
论文作者
论文摘要
如果每个非分类单纯形的代表映射为degerwise，则简单集是非单位的。简单映射集$ x^k $具有$ n $ -simplices由简单地图$Δ[n] \ times k \ to x $给出。我们证明，每当$ x $是非singular时，$ x^k $都是非单一的。因此，非单明一角的简单组构成了具有所有限制和colimits的笛卡尔封闭类别，但这不是拓扑。
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 $Δ[n] \times K \to X$. 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.
