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Jon Awbrey (May 31 2021 at 14:15):Prompted by Saunders Mac Lane's comment about “purloining words from the philosophers” — I know many people take that as tongue-in-cheek but I take him at his words, purloined or otherwise — I began a sketch several years ago inquiring into the continuities of the category concept through history. Clearly, there are wide divergences in the names and numbers of categories coming from different categorizers, so we don't expect to find much continuity there, but in the common function of category markers.
Here's a couple of links to what I've cobbled together so far —
🙞 Precursors Of Category Theory
🙞 Survey of Precursors Of Category Theory
Regards,
Jon
Fawzi Hreiki (May 31 2021 at 15:08):I would say also definitely Alfred North Whitehead. His ‘definition’ of the notion of a point in space is eerily close to locale theory.
Fawzi Hreiki (May 31 2021 at 15:09):He defines a point in a space as a kind of imaginary limit of extended regions
Fawzi Hreiki (May 31 2021 at 15:10):With the dynamically extended regions/events playing the dominant role and the points (of space or time) emerging as constant idealisations
Fawzi Hreiki (May 31 2021 at 15:12):Also Bergson’s ‘synthetic’ approach to experience with the idea that we understand dynamic experiences by ‘probing them’
Fawzi Hreiki (May 31 2021 at 15:13):So the thing is in itself totally synthetic and whole with our understanding of it coming from the ways we see it in different contexts.
Jon Awbrey (May 31 2021 at 15:16):I used to take another crack (or whack?) at Kant every decade or so ... but it doesn't look like I'll be getting back that way again so I'll leave that to someone else to fill in ...
Tom Hirschowitz (May 31 2021 at 19:15):@Jon Awbrey IIRC the introduction of Moerdijk and Reyes's Models for smooth infinitesimal analysis mentions Sophus Lie, in a way that might make him count as a precursor. Up to you!
Jon Awbrey (May 31 2021 at 19:54):@Tom Hirschowitz Absolutely! Lie gave me all the best clues to the maze of Differential Logic.
David Michael Roberts (Jun 01 2021 at 06:44):It is all in Dedekind... (well, not really, but his paper with the definition of the natural numbers is very structural, and Lawvere is very justified in attaching Dedekind's name the the concept of NNO.)
Fawzi Hreiki (Jun 01 2021 at 07:12):Dedekind and Cantor (along with Eilenberg and Mac Lane) are on the cover of Lawvere and Rosebrugh’s Sets for Mathematics
Javier Prieto (Jun 01 2021 at 11:42):The Erlangen Program is a pretty good candidate. Quoting wikipedia:
In the seminal paper which introduced categories, Saunders Mac Lane and Samuel Eilenberg stated: "This may be regarded as a continuation of the Klein Erlanger Program, in the sense that a geometrical space with its group of transformations is generalized to a category with its algebra of mappings"