Timeline for Projective resolutions in the wrong direction

6 events

when toggle format	what		by	license	comment
3 hours ago	history	became hot network question
8 hours ago	vote	accept	Frank
9 hours ago	answer	added	Jeremy Rickard		timeline score: 6
11 hours ago	comment	added	Ben Steffan		I don't follow the argument. Sure, there's a map, but the arrows in $P_\bullet$ do not magically change directions: You get a map from $P_0$ to $M$, and a map from $P_0$ to $P_1$, and a map from $P_1$ to $P_2$, etc. You seem to be suggesting that there should be a map $P_0 \to M$, and a map $P_1 \to P_0$, and a map $P_2 \to P_1$, but where are these wrong-way maps supposed to come from?
11 hours ago	comment	added	Aditya Dwivedi		I doubt when you say that $P_{\bullet}$ is a projective resolution in the usual sense. Since the map $P_{n-1} \to P_n$ is already surjective and $P_0 \to P_1$ is not injective, $P_{\bullet}$ is not a resolution.
11 hours ago	history	asked	Frank	CC BY-SA 4.0