Date: Sat, 23 May 1998 23:31:46 -0500
From: ralphw@math.uiuc.edu (Ralph Leonard Wojtowicz)


On pages 29--30 of "Categories for the Working 
Mathematician,"  MacLane reveals that "the discovery of
ideas as general as [categories, functors and natural
transformations] is chiefly the willingness to make a
brash or speculative abstraction, in this case supported
by the pleasure of purloining words from the philosophers:
`Category' from Aristotle and Kant, `Functor' from Carnap
and `natural transformation' from then current informal 
parlance."

Ideas from writings of Karl Marx are described in
"Conceptual Mathematics:  A First Introduction to Category
Theory,"  by Lawvere and Schanuel and elsewhere.


What orientation or program of study has philosophy given 
the investigation of mathematical categories?

Where could one begin reading to understand this influence?

Was selection of "monad" influenced by writings of Leibniz?


Thank you for your time.
					Sincerely,
					Ralph Wojtowicz