Geodesic
Classification of Constructible Cosheaves
Theory and applications of categories, Tome 35 (2020), pp. 1012-1047

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In this paper we prove an equivalence theorem originally observed by Robert MacPherson. On one side of the equivalence is the category of cosheaves that are constructible with respect to a locally cone-like stratification. Our constructibility condition is new and only requires that certain inclusions of open sets are sent to isomorphisms. On the other side of the equivalence is the category of functors from the entrance path category, which has points for objects and certain homotopy classes of paths for morphisms. When our constructible cosheaves are valued in Set we prove an additional equivalence with the category of stratified coverings.

Publié le :
Classification : 32S60, 18F20, 55N31, 58K99
Keywords: Constructible cosheaves, entrance path category, Reeb graphs, Reeb spaces 
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     author = {Justin Curry and Amit Patel},
     title = {Classification of {Constructible} {Cosheaves}},
     journal = {Theory and applications of categories},
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     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a26/}
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Justin Curry; Amit Patel. Classification of Constructible Cosheaves. Theory and applications of categories, Tome 35 (2020), pp. 1012-1047. http://geodesic.mathdoc.fr/item/TAC_2020_35_a26/