According to the Erdős Number Project (oakland.edu/enp/trivia), out of the 401k authors in MathSciNet, 268k authors are in the largest connected component of the collaboration graph (the graph with authors listed in MathSciNet as vertices and an edge between two authors if MathSciNet reports they have co-authored). So it's not surprising that you have a finite distance from these people.

The definition of $A \otimes B$ as a universal object in a category is treated in most graduate-level algebra books, e.g. Section IV.5 of Hungerford's Algebra. Here's a link: books.google.co.uk/…

Re line breaks, <br /> will force a line break.

This related question talks about the need for the axiom of choice: mathoverflow.net/questions/25375/…