presheaf of a topological basis

Let X be a topological spaceMathworldPlanetmath and let be a basis of its topologyMathworldPlanetmath. We can regard as a categoryMathworldPlanetmath with objects being the open sets in and arrows/morphisms between U,V to exists only if UV, and where the only element of (U,V) is the injection map UV. Let now 𝒞 be a complete category, we now define the presheafMathworldPlanetmathPlanetmathPlanetmath of C-objects over the basis B of the topology of X to be a contravariant functorMathworldPlanetmath

Title presheaf of a topological basis
Canonical name PresheafOfATopologicalBasis
Date of creation 2013-03-22 16:22:36
Last modified on 2013-03-22 16:22:36
Owner jocaps (12118)
Last modified by jocaps (12118)
Numerical id 14
Author jocaps (12118)
Entry type Definition
Classification msc 14F05
Classification msc 54B40
Classification msc 18F20
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