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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 10th 2011
   • (edited Jan 10th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexWhile working on [[cohesive (infinity,1)-topos]] I am running into the following situation in two places (in the discussion of concrete objects and of infinitesimal objects): It seems that the most natural thing that one would want to do in both cases is speak of a notion of $Y$ being a "subobject" of $X$ if a natural morphism $Y \to X$ in the game induces monomorphisms on all homotopy sheaves. Is there any good theory of such morphisms, and of factorizations through them?

   While working on cohesive (infinity,1)-topos I am running into the following situation in two places (in the discussion of concrete objects and of infinitesimal objects):

   It seems that the most natural thing that one would want to do in both cases is speak of a notion of $Y$ being a “subobject” of $X$ if a natural morphism $Y \to X$ in the game induces monomorphisms on all homotopy sheaves.

   Is there any good theory of such morphisms, and of factorizations through them?