In category theory, what does the $\otimes$ symbol mean?

Question

The Wikipedia page for Monoid includes the $\otimes$ symbol. Example:

In this question I see that this symbol is used to denote a tensor product.

What does $\otimes$ mean in the context of category theory?

It's part of the definition of a monoidal category (in much the same way "$\cdot$" is part of the definition of a group). — Daniel Schepler, Oct 23 '18 at 21:27
You know you can use MathJax in the title of your question, right? (Edited) — Alex Kruckman, Oct 23 '18 at 21:30

score 3 · Accepted Answer · answered Oct 23 '18 at 21:29

This is the tensor product (also known as the monoidal product) of the monoidal category in which the monoid lives.

The Wikipedia page you link to says:

...a monoid (or monoid object) $(M, \mu, \eta)$ in a monoidal category $(C, \otimes, I)$ is..."

So the meaning of $\otimes$ is being specified here. And if you click through to the page on monoidal category, you'll find out the definition.

1 Answers1