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Posina Venkata Rayudu (Aug 20 2023 at 07:00):If I may, in response to a discussion on Professor F. William Lawvere's Functorial Semantics, I came across syntax/semantics, which may be justified in that context, but in the context of Lawvere's functorial semantics:
not to forget the doctrine/monad that determines all of the above.
Posina Venkata Rayudu (Aug 22 2023 at 12:54):Posina Venkata Rayudu said:
If I may, in response to a discussion on Professor F. William Lawvere's Functorial Semantics, I came across syntax/semantics, which may be justified in that context, but in the context of Lawvere's functorial semantics:
not to forget the doctrine/monad that determines all of the above.
There are conceptual precursors to functorial semantics, which Professor F. William Lawvere discusses in his Perugia Notes (https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1972-perugia-lecture-notes.pdf) and in both of his textbooks: Conceptual Mathematics (with Schanuel) and Sets for Mathematics (with Rosebrugh), although may not be as explicitly as in Perugia Notes (and maybe somewhat like the Quality type (Definition 1 in his Axiomatic Cohesion; http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf) appearing (as Exercise 5 on p. 367) in the Conceptual Mathematics textbook. One of these days, I'll discuss these functorial semantics precursors due Cayley, Dedekind, and Yoneda (for now: they are all about representations/models/interpretations; while venting a bit on Frege for trying to palm off concepts as sets ;) Conceptual Mathematics, p. 380).