LTE on MathOverflow

Stream: condensed mathematics

[David Michael Roberts]

https://mathoverflow.net/q/415469/4177

Neil Strickland asking about BD and the simplifications the LTE has made possible. I gave some possibly ill-informed comments, to kick things off.

[Johan Commelin]

The comments already mostly answered the question, but I decided to write up a more detailed account of the story: https://mathoverflow.net/a/415540/21815

[Riccardo Brasca]

I admit I've always skipped all the details of the BD package, so I am very likely misunderstanding something, but looking at what you wrote, why can't one just take the zero complex for $C(A)$? Do we want surjectivity of at least the first map?

[Riccardo Brasca]

Ah, it's not functiorial, sorry.

[Johan Commelin]

To have a version of the BD lemma for a given package, you indeed need a bit more. Surjectivity of the first map is a necessary condition, yes.

[David Michael Roberts]

Thanks for that, @Johan Commelin , I completely skipped the distinction between "axiomatising the properties of the BD resolution" (which is what I thought had been done), and "axiomatising the properties of a BD package". I'm pretty sure I'd seen the first one written somewhere, but perhaps I had misread.

[Johan Commelin]

No worries. I admit that I chose ambiguous terminology.