2024/04/18 by Ana Luiza Tenório, Tenório, Ana Luiza, Hugo Luiz Mariano +1
Mathematics · #06F07 #18A40 #18F10 #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2404.12313
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a generalization of Grothendieck pretopologies -- suited for semicartesian categories with equalizers C -- leading to a closed monoidal category of sheaves, instead of closed cartesian category. This is proved through a different sheafification process, which is the left adjoint functor of the suitable inclusion functor but does not preserve all finite limits. If the monoidal structure in C is given by the categorical product, all constructions coincide with those for Grothendieck toposes. The motivation for such generalization stems from a certain notion of sheaves on quantales that does not form a topos.