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ralphwï¼ math.uiuc.edu

24 May 1998 24 May '98
4:31 a.m.

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

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