nLab
internal antisymmetric relation

Contents

Contents

Idea

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.

Definitions

In a finitely complete category CC, an internal antisymmetric relation is an internal relation R(s,t)X×XR\stackrel{(s,t)}\hookrightarrow X \times X on an object XX with a monomorphism α:R× XR opX\alpha:R \times_X R^\op \hookrightarrow X into the diagonal subobject XX, where R× XR opR \times_X R^\op is the pullback of the internal relation (s,t)(s,t) and its opposite internal relation (t,s)(t,s).

See also

Created on May 14, 2022 at 12:05:08. See the history of this page for a list of all contributions to it.