NYC Category Theory and Algebra is a group for people interested in studying Category Theory (CT) and/or Abstract Algebra together.
One of our purposes is to meet and read basic texts in Category Theory. We are currently reading Conceptual Mathematics by William Lawvere in reading group A and Categories in Context by Emily Riehl in reading group B. Next we'll read Awody's text or tackle MacLane's Categories for the Working Mathematician or Borceux's books. We'll also continue doing reading groups on introductory texts for newcomers.
Our other purpose will be to explore applied CT with texts including Category Theory for the Sciences by David Spivak, An Invitation to Applied Category Theory by Spivak and Brendan Fong, Tool and Object by Ralph Kromer, Picturing Quantum Processes by Koecke and Kissinger, to name a few. We'll be working on exercises together so we can build a useful foundation in applied CT together.
Likewise, for topics in Abstract Algebra.
My personal interest is in applying Category Theory / Algebra to Consciousness Science, but the group is open to any and all topics. Suggestions for applied topics are always welcome!
If you'd like to join our Slack Workspace to chat about Category Theory and post resources, message me with your email address. I'll invite you.
In this meeting series, we're reading through An Invitation to Applied Categry Theory: Seven Sketches in Compositionality. You can download a copy (v3, October 16, 2018) from here https://arxiv.org/abs/1803.05316.
Please finish chapter 4 and try out exercises under section 4.3.3 and section 4.5, and start on chapter 5 if you have time.
The proof I gave during last meeting on isomorhism (c ⊃ d) ≅ (¬c ∨ d) relies on universal constructions of (⊃), (¬) and (∨) is not quite related to the isomorhism (c ⊸ d) ≅ (c* ⊗ d) where (*) and (⊗) are not universal. So I attached another proof on that which appears a lot simpler.
If you've done any exercises or have organized talk on topics related to category theory, feel free to present during the meeting.