TITLE: Origin of the modern definition of the tensor product
QUESTION [10 upvotes]: Due to whom is the modern (i.e. via its universal property) definition of the tensor product, and in which article was it communicated?

REPLY [14 votes]: My recollection agrees with Mariano. Here's an except from Weibel's History of homological algebra

and from p. 172 of Mac Lane's Homology

and from Whitney's Collected Papers v. 1