For $C$ a category, a class$K \subset Mor(C)$ of morphisms in $C$ is said to satisfy 2-out-of-3 if for all composable $f,g \in Mor(C)$ we have that if two of the three morphisms $f$, $g$ and the composite $g \circ f$ is in $K$, then so is the third.

we have that if two of $f$, $g$ and $h$ are in $C$, then so is the third.

Examples

The class of isomorphisms in any category satisfies 2-out-of-3. This case is the archetype of most of the cases in which the property is invoked: 2-out-of-3 is characteristic of morphisms that have a notion of inverse.