Remote Access Transactions of the American Mathematical Society
Green Open Access

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

DOI: https://doi.org/10.1090/S0002-9947-1986-0833712-3
Article copyright: © Copyright 1986 American Mathematical Society