I found this proof here but I don't understand what they mean when they say that the existence of $C \to Q$ is implied by assumption? What assumption exactly? Can someone explain?
2026-03-28 01:06:47.1774660007
Confusion regarding proof of tensor products preserve cokernels
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The assumption is that $C$ is the cokernel of $A \to B.$ This way, any map $B \to Q$ such that $A \to B \to Q$ is zero uniquely factors through a map $C \to Q.$ Here this is applied to the "part" of $F$ which maps $B$ to $Q$.