The obstruction to an automorphism of a filtered ring

This paper sketches the proofs that (1) an automorphism of a complete filtered ring is a limit of successive approximations, (2) given an nth order approximate automorphism, there is an obstruction to prolonging it to an (n + l)st order approximation, the obstruction lying in a certain 2nd cohomology group, and (3) the mapping which sends an nth order approximate automorphism to its obstruction is a crossed homomorphism from the multiplicative group of nth order approximate automorphisms to the (additive) 2nd cohomology group containing the obstructions. The rings in question need not be associative: we tacitly assume that there is given a "category of interest," 6, in the sense of [l ] (which may be, in particular, the category of associative, Lie, or commutative associative rings), and "ring" and "morphism" are meant relatively to