Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
The notion of an internal antisymmetric relation is the generalization of that of antisymmetric relations as one passes from the ambient category of sets into more general ambient categories with suitable properties.
In a finitely complete category $C$, an internal antisymmetric relation is an internal relation $R\stackrel{(s,t)}\hookrightarrow X \times X$ on an object $X$ with a monomorphism $\alpha:R \times_X R^\op \hookrightarrow X$ into the diagonal subobject $X$, where $R \times_X R^\op$ is the pullback of the internal relation $(s,t)$ and its opposite internal relation $(t,s)$.
Created on May 14, 2022 at 16:05:08. See the history of this page for a list of all contributions to it.