Path-lifting for Grothendieck toposes

Moerdijk, Ieke

doi:10.1090/S0002-9939-1988-0920980-X

Path-lifting for Grothendieck toposes
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Proc. Amer. Math. Soc. 102 (1988), 242-248 Request permission

Addendum: Proc. Amer. Math. Soc. 125 (1997), 2815-2818.

Abstract:

A general path-lifting theorem, which fails in the context of topological spaces, is shown to hold for toposes, for locales (a slight generalization of topological spaces), and hence for complete separable metric spaces. This result generalizes the known fact that any connected locally connected topos (respectively complete separable metric space) is path-connected.

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