Cosheaves and homology
نویسندگان
چکیده
منابع مشابه
Classification of Constructible Cosheaves
Informally speaking, a map is stratified if it is proper and there is a partition S of X into manifolds so that over each manifold S ∈ S the map f(S)→ S is a fiber bundle. One perspective on this question uses the open sets of X to define a functor F̂ : Open(X)→ Set that assigns to each open U the set π0(f (U)) of path components. This functor satisfies a gluing axiom reminiscent of the usual va...
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We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...
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The localic definitions of cosheaves and connectedness are transferred from impredicative topos theory to predicative formal topology. A formal topology is locally connected (has base of connected opens) iff it has a cosheaf π0 together with certain additional structure and properties that constrain π0 to be the connected components cosheaf. In the inductively generated case, complete spreads (...
متن کاملJustin Curry, Foundations of TDA:Classification of Constructible Cosheaves
In my last talk I presented a poset-theoretic perspective on the Elder rule, which associates a barcode (persistence diagram) to a persistent set. In this talk, I will describe a quiver and representation-theoretic perspective on persistence that emerges from a classification theorem for constructible cosheaves originally described by MacPherson and proved in various versions by Shepard, Treuma...
متن کاملRelative (co)homology of $F$-Gorenstein modules
We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1968
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1968.25.1