nLab
(0,1)-category theory
Context
$(0,1)$ -Category theory
(0,1)-category theory : logic , order theory

(0,1)-category

proset , partially ordered set (directed set , total order , linear order )

lattice , semilattice

lattice of subobjects

complete lattice , algebraic lattice

distributive lattice , completely distributive lattice , canonical extension

hyperdoctrine

(0,1)-topos

Heyting algebra

frame , locale

Theorems Stone duality

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

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

higher category theory

Created on March 15, 2012 at 15:26:24.
See the history of this page for a list of all contributions to it.