In the context of higher category theory / (n,r)-categories, a poset is equivalently regarded as a (0,1)-category.
-categories play a major role in logic, where their objects are interpreted as propositions, their morphisms as implications and limits/products and colimits/coproducts as logical conjunctions and and or, respectively.
Dually, -categories play a major role in topology, where they are interpreted as categories of open subsets of a topological spaces, or, more generally, of locales.
Clearly, much of category theory simplifies drastically when restricted to -categories, but it is often most useful to make the parallel explicit.
higher category theory
Created on March 15, 2012 15:26:24
by Urs Schreiber