subobject
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Subobject — In category theory, there is a general definition of subobject extending the idea of subset and subgroup.In detail, suppose we are given some category C and monomorphisms: u : S rarr; A and: v : T rarr; A . We say u factors through v and write :… … Wikipedia
Subobject classifier — In category theory, a subobject classifier is a special object Omega; of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Omega;. As the name suggests, what a subobject classifier does is to… … 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
Substructure — In universal algebra, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are the traces of the functions and relations of the bigger structure … Wikipedia
Short five lemma — In mathematics, especially homological algebra and other applications of Abelian category theory, the short five lemma is a special case of the five lemma.It states that for the following commutative diagram (in any Abelian category, or in the… … Wikipedia
Galois connection — In mathematics, especially in order theory, a Galois connection is a particular correspondence between two partially ordered sets (posets). Galois connections generalize the correspondence between subgroups and subfields investigated in Galois… … Wikipedia
List of category theory topics — This is a list of category theory topics, by Wikipedia page. Specific categories *Category of sets **Concrete category *Category of vector spaces **Category of graded vector spaces *Category of finite dimensional Hilbert spaces *Category of sets… … Wikipedia
William Lawvere — Francis William Lawvere (b. February 9, 1937 in Muncie, Indiana) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.BiographyBorn February 9, 1937 in Muncie, Indiana, Lawvere studied continuum … Wikipedia
Categorical logic — is a branch of category theory within mathematics, adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science. In broad terms, categorical logic represents both syntax and semantics by a category,… … Wikipedia
List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… … Wikipedia
