Abstract
A mapping between two inverse systems f: X → Y, consisting of spaces X λ , and Y µ , respectively, is a commutative diagram, which contains the two systems X, Y as subdiagrams, and also contains a collection of mappings f µ : X λ , → Y µ . Coherent mappings modify mappings of inverse systems. They include all the data of a mapping of systems. However, instead of requiring commutativity of the diagram, one has, as additional data, homotopies which relate the mappings f µ and the bonding mappings of the systems X, Y, making the diagram commutative up to homotopy. Moreover, these homotopies are related by homotopies of higher order, which also make part of the data of a coherent mapping. Composition of coherent mappings and the identity mappings are defined, but they do not form a category.
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Mardešić, S. (2000). Coherent mappings. In: Strong Shape and Homology. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13064-3_2
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DOI: https://doi.org/10.1007/978-3-662-13064-3_2
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