Completions and Simplicial Complexes
In this paper, we first introduce the notion of a completion. Completions are inductive properties which may be expressed
in a declarative way and which may be combined. In the sequel of the paper, we show that completions may be used for describing
structures or transformations which appear in combinatorial topology. We present two completions, 〈 Cup 〉 and 〈 Cap 〉, in order to define, in an axiomatic way, a remarkable collection of acyclic complexes. We give few basic properties of
this collection. Then, we present a theorem which shows the equivalence between this collection and the collection made of
all simply contractible simplicial complexes.