fibred category
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Fibred category — Fibred categories are abstract entities in mathematics used to provide a general framework for descent theory. They formalise the various situations in geometry and algebra in which inverse images (or pull backs) of objects such as vector bundles … Wikipedia
Timeline of category theory and related mathematics — This is a timeline of category theory and related mathematics. By related mathematics is meant first hand * Homological algebra * Homotopical algebra * Topology using categories, especially algebraic topology * Categorical logic * Foundations of… … Wikipedia
Stack (descent theory) — In mathematics a stack is an abstract entity used to formalise some of the main concepts of descent theory. Descent theory is concerned with generalisations of situations where geometrical objects (such as vector bundles on topological spaces)… … Wikipedia
Moduli space — In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as… … Wikipedia
Forgetful functor — In mathematics, in the area of category theory, a forgetful functor is a type of functor. The nomenclature is suggestive of such a functor s behaviour: given some object with structure as input, some or all of the object s structure or properties … Wikipedia
Algebraic stack — In algebraic geometry, an algebraic stack is a concept introduced to generalize algebraic varieties, schemes, and algebraic spaces. They were originally proposed in a 1969 paper[1] by Pierre Deligne and David Mumford to define the (fine) moduli… … Wikipedia
List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… … Wikipedia
Image (mathematics) — In mathematics, the image of a preimage under a given function is the set of all possible function outputs when taking each element of the preimage, successively, as the function s argument. DefinitionIf f : X → Y is a function from set X to set… … Wikipedia
Stack (mathematics) — Stack in mathematics refers to two category theoretical concepts, which are connected to each other: * Stack in general is a fibred category that satisfies sheaf type glueing axioms; they are a key concept in in formalising descent theory *… … Wikipedia
Pullback — The notion of pullback in mathematics is a fundamental one. It refers to two different, but related processes: precomposition and fiber product.PrecompositionPrecomposition with a function probably provides the most elementary notion of pullback … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
