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Category of sets with a subdomain system, and germs of functions

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  • whrowan@member.ams.org
    I have defined this category and am using it in a project I am working on. I wonder if anyone has seen anything similar in the literature. The idea is that
    Message 1 of 1 , Sep 5, 2001
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      I have defined this category and am using it in a project I am
      working on. I wonder if anyone has seen anything similar in the
      literature. The idea is that you have a set, with a filter of
      subsets (which I call subdomains). That is, a pair <S,D> where
      D is a filter of subdomains. We then define a category LPartial,
      with objects such pairs <S,D>, for which the arrows from
      <S,D> to <T,D'> are partial functions from S to T, defined on
      some subdomain in D, which are local in the sense that if you
      have a subdomain in D', there is a subdomain in D which maps into
      it under the partial function. We call this the category of
      local partial functions. The arrows in the category of germs
      are then equivalence classes of local partial functions, where two
      local partial functions are considered equivalent if they agree on
      some subdomain.

      Has anyone seen this construction, especially in the context of
      universal algebra?

      Bill Rowan
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