Abstract
We introduce the notion of a system X=(Xa,pab,(A,⪯)) in a category C where (A,⪯) is a pre-ordered directed set, for each a∈A, Xa∈Obj(C), and whenever a⪯b there is defined a unique C-morphism pab:Xb→Xa. If a system admits certain commutative diagrams of a type defined in this paper, then it is called a delay-inverse system. In these systems the usual commutative diagrams pac=pabpbc when a⪯b⪯c of an inverse system might fail. However, commutativity is always recovered “after some delay.” The authors encountered, accidentally, a profuse class of naturally occurring delay-inverse systems that are not inverse systems in their study of certain classes of Čech systems and their relation to approximate systems in the sense of Mardešić and Watanabe.
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