Definition:Category with Products

Definition
Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is said to have products or to be a (meta)category with products iff:


 * For all sets of objects $\mathcal C \subseteq \mathbf C_0$, there is a product $\displaystyle \prod \mathcal C$ for $\mathcal C$.

Also known as
Some authors, sensibly perhaps, say $\mathbf C$ as above has small products.

As it is rare that products are taken over collections too large to be sets, the standard terminology has deemed this abuse of language admissible.

Also see

 * Complete Category