2-Out-Of-3 Property

Let π’ž π’ž \mathcal{C} be a category, and β„³ βŠ† π’ž β„³ π’ž \mathcal{M}\subseteq\mathcal{C} be a subset of morphisms. We say that β„³ β„³ \mathcal{M} satisfies 2-out-of-3 or 3-for-2 if for all f : π’ž ⁒ ( Y , Z ) : 𝑓 π’ž π‘Œ 𝑍 f:\mathcal{C}(Y,Z) , g : π’ž ⁒ ( X , Y ) : 𝑔 π’ž 𝑋 π‘Œ g:\mathcal{C}(X,Y) , if any 2 of f , g , f ∘ g 𝑓 𝑔 𝑓 𝑔 f,g,f\circ g are in β„³ β„³ \mathcal{M} , then the 3rd is as well.