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Posets form a poset enriched category

  1. Nov 4, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove that Poset can be viewed as a Poset-enriched category


    2. Relevant equations
    A category C is enriched in another category D if the hom-objects of C are objects in D. Alternatively, C is D enriched if for any two objects , A,B in C, hom(A,B) constitutes an object of D

    A poset is a category with at most one map from an object D to another E.

    3. The attempt at a solution
    I think I am having trouble understanding what to prove here.

    So we need to show that hom(A,B) is a poset. But since A and B are categories (with one arrow between any two objects), then hom(A,B) is the functor category. In otherwords we must show that there can be only one natural transformation between any two functors in hom(A,B).

    Is it fair to say that a proof of the above is sufficient?
     
  2. jcsd
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