Cf: Higher Order Sign Relations • 6
::: Cliff Joslyn ( https://groups.google.com/g/cybcom/c/UwInmSnuv0c/m/w9ncBWKUAAAJ
Cliff Joslyn recommended the following books.
• Spivak, David I. (2014), Category Theory for the Sciences
• Fong, Brendan, and Spivak, David I. (2019),
An Invitation to Applied Category Theory : Seven Sketches in Compositionality
Dear Cliff, All,
The following Survey page gives a hint of the tack I've been taking with
category theory since the early days but definitely moving into higher gear
during my year at Illinois in the mid 1980s. John Gray taught a course joint
between math and computer science on the Applications of Lambda Calculus and
David Plaisted taught a course on Resolution-Unification Theorem Proving, both
of which I took and followed up with independent studies. I spent a heady year
making the circuit between math, computer science, and psychology departments
and a lot of what I work on today goes back to issues raised in those days.
• Survey of Precursors Of Category Theory
I know that Survey from a couple years ago still looks a little sketchy
but I'll be working to make it less so as time goes by, especially if
I ever get around to unpacking my notes from the basement boxes.
I have managed to sample contemporary approaches to categories at sundry
sites around the web over the last couple of decades — John Baez, nCafe,
nLab, Zulip Category Chat, Topos Group, etc. As great as all that is
there's a reason why it bears but tangentially on the issues I've been
pursuing. That has to do with the Peirce Factor and how far a given
line of inquiry takes account of it.
As luck would have it, one of the texts John Gray used for his course,
Lambek and Scott's “Introduction to Higher Order Categorical Logic”,
resonated strongly with themes I knew from Peirce and that led me
to many adventures of ideas still in progress. The following set
of excerpts I shared with the Standard Upper Ontology Group back
in the day may suggest the character of that work.
• Lambek, J. and Scott, P.J. (1986),
Introduction To Higher Order Categorical Logic
• Excerpts ( https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes#HOC
• Discussion ( https://oeis.org/wiki/User:Jon_Awbrey/Mathematical_Notes#HOC_Discuss
There's a lot more to say, but that's all I have time for today …