2016/05/05 by Andrei V. Prasolov, Prasolov, Andrei V. · 1 citation
Mathematics · #14F20 #18F20 #55Q07 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18F10 #Secondary 55P55
paper · pdf · doi:10.48550/arxiv.1605.01555
openalex publication_date 2016/05/05 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
It is proved that for any Grothendieck site X, there exists a coreflection (called cosheafification) from the category of precosheaves on X with values in a category K, to the full subcategory of cosheaves, provided either K or Kop is locally presentable. If K is cocomplete, such a coreflection is built explicitly for the (pre)cosheaves with values in the category Pro% ( K) of pro-objects in K. In the case of precosheaves on topological spaces, it is proved that any precosheaf with values in Pro( K) is smooth, i.e. is strongly locally isomorphic to a cosheaf. Constant cosheaves are constructed, and there are established connections with shape theory.