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?

Answer 1

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.