Category Theory

Last updated: Sun, 25 Nov 2018

\(P_1\) along with \(X\) and \(Y\) defines a product. There exists a morphism between \(P_1\) and \(P_2\) preserving the product structure.

\[ \begin{xy} \xymatrix{ P_2 \ar@/_/[ddr]_y \ar@{.>}[dr]|{\exists!} \ar@/^/[drr]^x \\ & P_1 \ar[d]^q \ar[r]_p & X \\ & Y & } \end{xy} \]