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    Partially-Ordered Sets ( Posets ) and Hom-sets

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    Show that a poset (partially-ordered set) is the same thing as a category in which all Hom-sets have at most one element.

    © BrainMass Inc. brainmass.com October 9, 2019, 5:58 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/partially-ordered-sets-posets-hom-sets-74072

    Solution Preview

    This is only true if we consider isomorphic objects in a category to be the same.
    If we have such a category C then define a partial order on the set of objects
    O : a <= b iff there is a morphism from a to b.
    If a <= b and b <= c, then we can compose the morphisms to ...

    Solution Summary

    Partially-Ordered Sets ( Posets ) and Hom-sets are investigated. The solution is detailed and well presented.

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