Let (A_{n}) be an inverse system of abelian groups. The following are equivalent

- (A
_{n}) is zero as a pro-object, - lim A
_{n}= 0 and R^{1}lim A_{n}= 0 and the same holds for ⨁_{i ∈ N}(A_{n}).

See Tag 091C.

Let (A_{n}) be an inverse system of abelian groups. The following are equivalent

- (A
_{n}) is zero as a pro-object, - lim A
_{n}= 0 and R^{1}lim A_{n}= 0 and the same holds for ⨁_{i ∈ N}(A_{n}).

See Tag 091C.