Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 18B25, 54D05

Retrieve articles in all journals with MSC: 18B25, 54D05

Additional Information

PII: S 0002-9947(1986)0833712-3
Article copyright: © Copyright 1986 American Mathematical Society