Crossed complexes and chain complexes with operators ∗ by RONALD BROWN
نویسنده
چکیده
Chain complexes with a group of operators are a well known tool in algebraic topology, where they arise naturally as the chain complex C∗X̃ of cellular chains of the universal cover X̃ of a reduced CW -complex X. The group of operators here is the fundamental group of X. J.H.C. Whitehead in his classical but little read paper [31] showed that the chain complex C∗(X̃) is useful for the homotopy classification of maps between non-simply connected spaces (see below). His methods must have seemed at the time to be circuitous. In modern parlance, he introduced the categories CW of CW -complexes, HS of homotopy systems, and FCC of free chain complexes with operators, together with functors1
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