Connected locally connected toposes are path-connected

Moerdijk, I.; Wraith, G. C.

doi:10.1090/S0002-9947-1986-0833712-3

Connected locally connected toposes are path-connected
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by I. Moerdijk and G. C. Wraith

Trans. Amer. Math. Soc. 295 (1986), 849-859

DOI: https://doi.org/10.1090/S0002-9947-1986-0833712-3

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Abstract:

A conjecture of A. Joyal is proved, which states that, in contrast to topological spaces, toposes which are connected and locally connected are also path-connected. The reason for this phenomenon is the triviality of cardinality considerations in the topos-theoretic setting; any inhabited object pulls back to an enumerable object under some open surjective geometric morphism. This result points towards a homotopy theory for toposes.

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