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Connected Locally Connected Toposes are Path-Connected
I. Moerdijk and G. C. Wraith
Transactions of the American Mathematical Society
Vol. 295, No. 2 (Jun., 1986), pp. 849-859
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2000067
Page Count: 11
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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.
Transactions of the American Mathematical Society © 1986 American Mathematical Society