Associations to the word «Pushout»

PUSHOUT, noun. (category theory) Given a pair of morphisms \(f:Z\rightarrow X\) and \(g: Z\rightarrow Y\) with a common domain, Z, their pushout is a pair of morphisms \(i_1:X\rightarrow P\) and \(i_2:Y\rightarrow P\) as well as their common codomain, P, such that the equation \( i_1 \circ f = i_2 \circ g\) is satisfied, and for which there is the universal property that for any other object Q for which there are also morphisms \(j_1: X\rightarrow Q\) and \(j_2: Y\rightarrow Q\); there is a unique morphism \(u: P\rightarrow Q\) such that \( u \circ i_1 = j_1\) and \(u \circ i_2 = j_2\).