Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
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.
In a finitely complete category $C$, a partially ordered object is a preordered object $(X, R, s, t, \rho, \tau_p)$ such that the internal preorder $R\stackrel{(s,t)}\hookrightarrow X \times X$ is an internal antisymmetric relation.
Last revised on May 14, 2022 at 12:10:05. See the history of this page for a list of all contributions to it.