A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  My notes on the project are still very rough and incomplete but I find myself returning to them from time to time.

Preamble

Now the discovery of ideas as general as these 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 (Logische Syntax der Sprache), and “natural transformation” from then current informal parlance.

— Saunders Mac Lane • Categories for the Working Mathematician

Resources

• Precursors Of Category Theory
• Propositions As Types Analogy
• Survey of Precursors Of Category Theory

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