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 September 20, 2018, 4:20 pm ad1c9bdddf - https://brainmass.com/math/discrete-math/partially-ordered-sets-posets-hom-sets-74072
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 ...
Partially-Ordered Sets ( Posets ) and Hom-sets are investigated. The solution is detailed and well presented.