# Where did the notion of the product in a category first appear?

In his book, Category Theory[1], Awodey writes the following about it:

Next, we are going to see the categorical definition of a product of two objects in a category. This was first given by Mac Lane in 1950, and it is probably the earliest example of category theory being used to define a fundamental mathematical notion.

In the last editions of Algebra[2] and Categories for the Working Mathematician[3], the notion of product in a category is presented (of course). I was wondering how did MacLane first arrive at and where did he publish this notion?

References:

[1] Awodey, Steve: Category Theory. Oxford University Press, 2010.
[2] Mac Lane, Saunders and Birkhoff, Garrett: Algebra. AMS Chealsea Publishing, 1999.
[3] Mac Lane, Saunders: Categories for the Working Mathematician. Springer, 1998.

"Let $A\times B$ be the direct (or Cartesian) product of the groups $A$ and $B$, defined as the group of pairs $(a, b)$ for $a\in A$ and $b\in B$. Let $\alpha$ and $\beta$ denote the natural homomorphisms $\alpha(a, b)=a$, $\beta(a, b)=b$ of the direct product onto its respective factors. The direct product may then be described conceptually in terms of $\alpha$ and $\beta$ and the diagram [the now familiar one, labeled (3.1)] as follows. Given any group $C$, and any homomorphisms $\alpha'$ and $\beta'$ of $C$ into $A$ and $B$ respectively, there exists one and only one homomorphism $\gamma: C\to A$ with $\alpha\gamma=\alpha'$ and $\beta\gamma=\beta'$... This property of the diagram (3.1) determines the direct product $A\times B$ and its mappings $\alpha$ and $\beta$ up to an isomorphism; hence it may serve as a definition of the direct product."