So one of the things I’ve been doing recently is finishing up a version, and talking about, this paper which I’ve now put on the arXiv. While at it, I figured I should update a previous paper – the current version cuts out part of the original subject (cobordism categories) and expands on the category-theory side of things, giving more detailed proofs, etc. That part will then be out of the way when the topology side shows up in another paper, yet to appear, which will also use the stuff about 2-vector spaces and groupoids from the “new” paper.
Ironically, although I fixed the “issue” which arose when I was posting on the subject – and I’ll come back to that – I’ve already talked about most of what’s in the “new” paper, whereas I never got around to talking about what’s in the “old” one, updated version or not. That’s the one called “Double Bicategories and Double Cospans”, which is the most strictly category-theoretic thing I’ve produced: all the motivation from physics has been abstracted away. So when I have some time, I’ll write something about that one.
For now, I just wanted to link to this new stuff.