TITLE: What is the categorical diagram for the tensor product?
QUESTION [13 upvotes]: The title says it all: what is the diagram that defines a tensor product?  (I'm using the term diagram here in the technical sense it has in category theory.)
Edit: This question was motivated by the following statement:  "...all limits and colimits are initial objects somewhere, and we can even sort of take the view that all universal properties are initial objects somewhere", from this video (@~9:15)
Thanks!

REPLY [4 votes]: From http://maths.mq.edu.au/~street/PlanarDiags.pdf:


as well as other conditions.