germ of homomorphisms

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Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… … Wikipedia
Direct limit — In mathematics, a direct limit (also called inductive limit) is a colimit of a directed family of objects . We will first give the definition for algebraic structures like groups and modules, and then the general definition which can be used in… … Wikipedia
Local ring — In abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called local behaviour , in the sense of functions defined on varieties or manifolds, or of… … Wikipedia
Cohomology — In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries.… … Wikipedia

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