Sheaf theory

collection of objects associated to subsets of a space in a manner admitting gluing and restriction

mathematical function

contravariant functor to the category of sets and functions

In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion of localization. The Grothendieck topoi find applications in algebraic geometry, and more general elementary topoi are used in logic.

equivalence class of objects sharing local properties at a point in a topological space

semantics for modal logics

space together with a sheaf of rings

sheaf of abelian groups, whose sections are modules over a sheaf of rings

structure on a category C which makes the objects of C act like the open sets of a topological space

In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order. Hyperfunctions were introduced by Mikio Sato in 1958 in Japanese, (1959, 1960 in English), building upon earlier work by Laurent Schwartz, Grothendieck and others.

right derived functors of the global sections functor Γ: AbSh → Ab

type of sheaf

finite-type sheaf F of modules over a ringed space such that the kernel of a surjective morphism from a finite direct sum of the structure sheaf onto it is also of finite type

technique of studying linear partial differential equations

sheafification of the constant presheaf

creating a meromorphic function in multiple variables

stalk of a sheaf in mathematics

In mathematics, a '''D-module' is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since around 1970, D''-module theory has been built up, mainly as a response to the ideas of Mikio Sato on algebraic analysis, and expanding on the work of Sato and Joseph Bernstein on the Bernstein–Sato polynomial.

subsheaf (as a sheaf of modules) of the structure sheaf of a scheme (or ringed space)