Hi, Rajesh! What sort of talks are there at Brendan and David's seminar? Brendan hasn't told me about it..
Here are some shoot-from-the-hip comments about your ideas:
1. I think there's great potential for using category theory in _all_ branches of science, because it's sort of "Set theory 2.0" - that is, a comprehensive framework for formalizing things, which subsumes and goes far beyond set theory. But it takes a lot of work to exploit this potential: a good solid knowledge of category theory, a good solid knowledge of the intended application, and a lot of time spent figuring out how to connect them. It could work better with two people - a category theorist who knows a bit about the intended application and an expert in the intended application who knows some category theory - but they would need to be committed to it. I've been focusing on applications where I can play both parts.
2. The categorical approach to logic is deeply philosophical at its core: it's based on new insights that go beyond the early 20th century work by Russell, Zermelo, Frenkel, von Neumann, Gödel _et al_. Some of the ideas are introduced in Elaine Landry's book _[Categories for the Working Philosopher](https://global.oup.com/academic/product/categories-for-the-working-philosopher-9780198748991?cc=us&lang=en&)_. Have you read that?