monic morphism
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Monic — In mathematics, monic can refer to monic morphism a special kind of morphism in category theory. monic polynomial a polynomial whose leading coefficient is one. In linguistics, monic can refer to Monic languages This disambiguation page lists… … Wikipedia
Morphism — In mathematics, a morphism is an abstraction derived from structure preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear… … Wikipedia
Étale morphism — In algebraic geometry, a field of mathematics, an étale morphism (pronunciation IPA|) is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem,… … Wikipedia
Monomorphism — This page is about the mathematical term. For other uses, see Monomorphic (disambiguation) or Polymorphism (disambiguation). In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from … Wikipedia
Topos — For topoi in literary theory, see Literary topos. For topoi in rhetorical invention, see Inventio. In mathematics, a topos (plural topoi or toposes ) is a type of category that behaves like the category of sheaves of sets on a topological space.… … Wikipedia
Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… … Wikipedia
Glossary of category theory — This is a glossary of properties and concepts in category theory in mathematics.CategoriesA category A is said to be: * small provided that the class of all morphisms is a set (i.e., not a proper class); otherwise large. * locally small provided… … Wikipedia
Allegory (category theory) — In mathematics, in the subject of category theory, an allegory is a category that has some of the structure of the category of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in… … Wikipedia
Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A … Wikipedia
Coproduct — This article is about coproducts in categories. For coproduct in the sense of comultiplication, see Coalgebra. In category theory, the coproduct, or categorical sum, is the category theoretic construction which includes the disjoint union of sets … Wikipedia
Image (category theory) — Given a category C and a morphism f:X ightarrow Y in C , the image of f is a monomorphism h:I ightarrow Y satisfying the following universal property: #There exists a morphism g:X ightarrow I such that f = hg . #For any object Z with a morphism k … Wikipedia
