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1. Category theory: Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory is used ... (General theory of mathematical structures) [100%] 2023-12-19 [Category theory] [Higher category theory]...
2. Category theory: Category theory is a branch of mathematics that studies and analyzes different types of mapping between sets. A category consists of a collection of objects, together with a collection of maps between those objects, called "morphisms", and a way to ... [100%] 2023-03-05 [Mathematics]
3. Category theory: Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory is used ... (General theory of mathematical structures) [100%] 2024-01-26 [Category theory] [Higher category theory]...
4. Category theory: Category theory is a relatively new birth that arose from the study of cohomology in topology and quickly broke free of its shackles to that area and became a powerful tool that currently challenges set theory as a foundation of ... [100%] 2024-01-26 [Category theory]
5. Category theory: Category theory is the mathematical field that studies categories, which are a certain kind of mathematical structure. Categories are found throughout mathematics, and category theory thus has many mathematical applications. [100%] 2023-06-24
6. Category theory: Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, category theory is ... (General theory of mathematical structures) [100%] 2023-12-18 [Category theory] [Higher category theory]...
7. Category theory: Category theory is a relatively new birth that arose from the study of cohomology in topology and quickly broke free of its shackles to that area and became a powerful tool that currently challenges set theory as a foundation of ... [100%] 2023-12-17 [Category theory]
8. Category Theory: Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science, and is also applied to mathematical physics. Roughly, it is a general mathematical theory of structures and of systems of structures. (Philosophy) [100%] 2021-12-24
9. Dual (category theory): In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category C. Given a statement regarding the category C, by interchanging the source and target ... (Category theory) [81%] 2024-01-26 [Category theory] [Duality theories]...
10. Limit (category theory): In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint unions, direct ... (Category theory) [81%] 2023-10-17 [Limits (category theory)]
11. Center (category theory): In category theory, a branch of mathematics, the center (or Drinfeld center, after Soviet-American mathematician Vladimir Drinfeld) is a variant of the notion of the center of a monoid, group, or ring to a category. The center of a ... (Category theory) [81%] 2023-11-28 [Category theory]
12. Pullback (category theory): In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a ... (Category theory) [81%] 2024-01-14 [Limits (category theory)]
13. Dual (category theory): In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category C. Given a statement regarding the category C, by interchanging the source and target ... (Category theory) [81%] 2023-12-30 [Category theory] [Duality theories]...
14. Presheaf (category theory): In category theory, a branch of mathematics, a presheaf on a category C {\displaystyle C} is a functor F : C o p → S e t {\displaystyle F\colon C^{\mathrm {op} }\to \mathbf {Set} } . If C {\displaystyle C} is the ... (Category theory) [81%] 2023-11-21 [Functors] [Sheaf theory]...
15. Allegory (category theory): In the mathematical field 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 ... (Category theory) [81%] 2023-12-07 [Category theory] [Mathematical relations]...
16. Envelope (category theory): In :Category theory and related fields of mathematics, an envelope is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or Stone–Čech compactification of a topological space. A dual construction is called ... (Category theory) [81%] 2023-11-02 [Category theory] [Duality theories]...
17. Presheaf (category theory): In category theory, a branch of mathematics, a presheaf on a category \displaystyle{ C }[/math] is a functor \displaystyle{ F\colon C^\mathrm{op}\to\mathbf{Set} }[/math]. If \displaystyle{ C }[/math] is the poset of open sets in a ... (Category theory) [81%] 2023-07-17 [Functors] [Sheaf theory]...
18. Cosmos (category theory): In the area of mathematics known as category theory, a cosmos is a symmetric closed monoidal category that is complete and cocomplete. Enriched category theory is often considered over a cosmos. (Category theory) [81%] 2024-01-13 [Category theory]
19. Pushout (category theory): In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y ... (Category theory) [81%] 2022-12-01 [Limits (category theory)]
20. Applied category theory: Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics (in particular quantum mechanics), natural language processing, control theory, probability theory and causality ... (Applications of category theory) [81%] 2023-10-17 [Category theory]
21. Nerve (category theory): In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C. The geometric realization of this simplicial set is a topological space, called ... (Category theory) [81%] 2023-12-27 [Category theory] [Simplicial sets]...
22. Higher category theory: In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category ... (Generalization of category theory) [81%] 2023-11-17 [Foundations of mathematics] [Higher category theory]...
23. Product (category theory): In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups ... (Category theory) [81%] 2024-01-07 [Limits (category theory)]
24. Kernel (category theory): In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f : X ... (Category theory) [81%] 2023-12-28 [Category theory]
25. Monad (category theory): In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors of some fixed category. An endofunctor is a functor mapping a category to itself, and ... (Category theory) [81%] 2024-01-14 [Adjoint functors] [Category theory]...
26. Product (category theory): In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups ... (Category theory) [81%] 2023-11-03 [Limits (category theory)]
27. Span (category theory): In category theory, a span, roof or correspondence is a generalization of the notion of relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered ... (Category theory) [81%] 2023-12-31 [Functors]
28. Monad (category theory): In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors. An endofunctor is a functor mapping a category to itself, and a monad is an ... (Category theory) [81%] 2023-05-08 [Adjoint functors] [Category theory]...
29. Cone (category theory): In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances in category theory as well. (Category theory) [81%] 2023-11-13 [Category theory] [Limits (category theory)]...
30. Kernel (category theory): In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel of the morphism f : X ... (Category theory) [81%] 2023-09-14 [Category theory]