# 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.

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