If you need an accessible version of this item please contact JSTOR User Support

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
DOI: 10.2307/2000067
Stable URL: http://www.jstor.org/stable/2000067
Page Count: 11
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Connected Locally Connected Toposes are Path-Connected
Preview not available

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.

Page Thumbnails

  • Thumbnail: Page 
849
    849
  • Thumbnail: Page 
850
    850
  • Thumbnail: Page 
851
    851
  • Thumbnail: Page 
852
    852
  • Thumbnail: Page 
853
    853
  • Thumbnail: Page 
854
    854
  • Thumbnail: Page 
855
    855
  • Thumbnail: Page 
856
    856
  • Thumbnail: Page 
857
    857
  • Thumbnail: Page 
858
    858
  • Thumbnail: Page 
859
    859