Re: On the etymology of the word "functor"

["George Janelidze" <janelg@telkomsa.net>]

Dear Colleagues,

Referring to Julian Rohrhuber's message of February 20: I don't think it is
a good idea to cut a sentence in the middle and then call it "somewhat
arrogant", especially when it is from a paper of Saunders Mac Lane. The full
sentence is:

"There was also some fun with the choice of terminology. Since the
philosopher Kant had made ample use of general categories, the term was
borrowed from him for its present mathematical use, while Camap, in his book
on Die Logische Syntax der Sprachen had talked of functors in a different
sense and made some corresponding mistakes. It seemed in order to take over
that word for a better and less philosophical purpose."

Let me also add a sentence from Mac Lane's paper "Samuel Eilenberg and
Categories" (JPAA 168, 2002, 127-131):

"Also the terminology was largely purloined: “category” from Kant, “natural”
from vector spaces and “functor” from Carnap. (It was used in a different
sense in Carnap’s influential book “Logical Syntax of Language”; I had
reviewed the English translation of the book (in the Bulletin, AMS) and had
spotted some errors; since Carnap never acknowledged my finding, I did not
mind using his terminology.)"

Referring to Michael Barr's message of February 19, which is:

"I don't know what is mysterious about the origin of functor.  It is a
2-function and they surely wanted to suggest a variant of function. But this
illustrates a point I have been trying to make for decades to so-called
mathematical historians.  While they have been grinding the origins of
calculus finer and finer, they are allowing contemporary history to
disappear.  If someone had interviewed Eilenberg or Mac Lane at length 30
years ago we would know why they chose functor.  And much much more.  Now
they are gone.  Bill Lawvere is gone.  There are still a few of the older
category theorists left, but probably not for long.  But this is why I have
been posting these historical notes."

So very true! However, this is not just about "so-called mathematical
historians", but also about certain mathematicians who tell historians what
is important in mathematics and what is not. And it is also about many of
us, who, for example, did nothing with the unthinkable article "Timeline of
category theory and related mathematics" in Wikipedia and a similar article
in nLab (well, both of them have a lot of good mathematics mentioned, but
putting 'selected good' and 'selected bad' together, might be the worst kind
of disinformation...).

George



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