Hi all,
Context: I've been thinking about the tower argument Lemma 2.21 https://arxiv.org/pdf/1803.10897.pdf in this paper (again, where I have previously asked) and figured I'm unclear about the following fact:
What is a criteria for checking if an object is prozero in Pro(Fun(C,Sp)), pro category of Fun(C,Sp)? It seems to me that the functora \pi_i :Pro(Fun(C,Sp)) -> Pro(Fun(C,Ab)) forms jointly conservative map?
If so, how does one see this?