"Categories for the Working Philosopher" is a recent book edited by Elaine Landry
with a number of articles on Category Theory, but quite a few on Homotopy Type Theory too,
as shown below:
1: The Roles of Set Theories in Mathematics,
Colin McLarty2: Reviving the Philosophy of Geometry,
David Corfi eld3: Homotopy Type Theory: A synthetic approach to higher equalities,
Michael Shulman4: Structuralism, Invariance, and Univalence,
Steve Awodey5: Category Theory and Foundations,
Michael Ernst6: Canonical Maps,
Jean-Pierre Marquis7: Categorical Logic and Model Theory,
John Bell8: Unfolding FOLDS: A Foundational Framework for Abstract Mathematical Concepts,
Jean-Pierre Marquis9: Categories and Modalities,
Kohei Kishida10: Proof Theory of the Cut Rule,
J.R.B Cockett and R.A.G Seely11: Contextuality: At the Borders of Paradox,
Samson Abramsky12: Categorical Quantum Mechanics I: Causal Quantum Processes,
Bob Coecke and Aleks Kissinger13: Category Theory and the Foundations of Classical Spacetime Theories,
James Weatherall14: Six-dimensional Lorentz Category,
Joachim Lambek15: Applications of Categories to Biology and Cognition,
Andrée Ehresmann16: Categories as Mathematical Models,
David I. Spivak17: Categories of Scientifi c Theories,
David Hans Halvorson and Dimitris Tsementzis18: Structural Realism and Category Mistakes,
Elaine Landry
available here:
https://global.oup.com/academic/product/9780198748991/?cc=uk&lang=en&promocode=AAFLYG6I have found the first 6 articles very helpful, and am going through in detail the articles on Model Theory and Modal Logic. The Modal
Logic looks at David Lewis type neighborhood semantics with a topoligical mapping. It looks like this may answer some
of the questions I asked a few years ago on this list.
Henry