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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Connected locally connected toposes are path-connected


Authors: I. Moerdijk and G. C. Wraith
Journal: Trans. Amer. Math. Soc. 295 (1986), 849-859
MSC: Primary 18B25; Secondary 54D05
MathSciNet review: 833712
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833712-3
PII: S 0002-9947(1986)0833712-3
Article copyright: © Copyright 1986 American Mathematical Society