nLab
partially ordered object

Contents

Context

Relations

Category theory

(0,1)(0,1)-Category theory

Contents

Idea

The notion of a partially ordered object is the generalization of that of partially ordered sets as one passes from the ambient category of sets into more general ambient categories with suitable properties.

Definitions

In a finitely complete category CC, a partially ordered object is a preordered object (X,R,s,t,ρ,τ p)(X, R, s, t, \rho, \tau_p) such that the internal preorder R(s,t)X×XR\stackrel{(s,t)}\hookrightarrow X \times X is an internal antisymmetric relation.

See also

Last revised on May 14, 2022 at 12:10:05. See the history of this page for a list of all contributions to it.