nLab (0,1)-category theory




In the context of higher category theory / (n,r)-categories, a poset is equivalently regarded as a (0,1)-category.

(0,1)(0,1)-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, (0,1)(0,1)-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 (0,1)(0,1)-categories, but it is often most useful to make the parallel explicit.

higher category theory

Created on March 15, 2012 at 15:09:29. See the history of this page for a list of all contributions to it.