Topos Institute

I think many people are coming at category theory with a feeling that it has interdisciplinary ramifications and offers a unifying lens on multiple topics. Specifically I think the topics that have all drawn me towards category theory in different ways are:

1. Philosophy and formal logic (and other structures that have surprising isomorphisms within math and science).
2. Functional programming, type theory, and lambda calculus (and how these represent a bridge between computer science and mathematics)
3. Knowledge graphs and other systems for modeling information (semantic triples, RDF, etc)

I think each of these has a strong community of interested people who sense there’s some insight to be gained from the category theory perspective. There are a number of good online lectures that introduce category theory, and some that begin to hint and push towards the interdisciplinary applications at an introductory level (Bartosz Milewski’s lectures come to mind, Richard Southwell’s also provide some intuition in that regard). But I haven’t found many (any?) resources that really push towards teaching category theory hand-in-hand with applications like the ones I’ve described above. The Topos Institute’s online lectures are close to providing this, but their specialized nature make it so it’s not easy to understand the implications of the lecture as relative lay-person.

I would really appreciate an introductory category theory series or course that has a strong eye towards the applications in the spaces described above. Alternatively, if these resources exist, it would be great to compile a syllabus to guide folks who want to learn from this angle (but don’t necessarily need to write papers of their own). There are many people who have an intuition for the importance of language, logic, ontologies, and “functional thinking”, and deep diving into how category theory provides a shared language for these areas I think would be very impactful.