Overview
Given two objects in a category, {% A %} and {% B %}, the product of {% A %} and {% B %} is an object {% P %} and two arrows {% p1 %} and {% p2 %}
{% A \overset{p1} \leftarrow P \overset{p2}\rightarrow B %}
such that, for any object {% T %} with arrows such as
{% A \overset{h} \leftarrow T \overset{k}\rightarrow B %}
there is a unique arrow {% u :T \rightarrow P %} that makes the diagram commute.