the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...
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categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer science also rely on category theory,...
34 KB (3,831 words) - 11:45, 30 October 2024
In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...
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higher category theory, the concept of higher categorical structures, such as (∞-categories), allows for a more robust treatment of homotopy theory, enabling...
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of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides...
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Conferences: Applied category theory Symposium on Compositional Structures (SYCO) Books: Picturing Quantum Processes Categories for Quantum Theory An Invitation...
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(PDF), Theory and Applications of Categories, 28: 332–370, arXiv:1209.3606, Bibcode:2012arXiv1209.3606L MacLane, Saunders (1978), Categories for the...
30 KB (4,469 words) - 12:20, 16 October 2024
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...
15 KB (1,978 words) - 02:10, 30 July 2024
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...
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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...
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In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...
28 KB (4,352 words) - 03:41, 22 March 2024
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...
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Functor (redirect from Functor (category theory))
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...
24 KB (3,513 words) - 19:52, 25 October 2024
use of categories. Category Functor Natural transformation Homological algebra Diagram chasing Topos theory Enriched category theory Higher category theory...
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Normal morphism (redirect from Normal (category theory))
In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism...
2 KB (280 words) - 15:46, 13 February 2022
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...
13 KB (1,941 words) - 22:41, 24 August 2024
In category theory, a branch of mathematics, the image of a morphism is a generalization of the image of a function. Given a category C {\displaystyle...
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traditional theory of categories, like linguist Eugenio Coseriu and other proponents of the structural semantics paradigm. In this prototype theory, any given...
31 KB (4,171 words) - 23:54, 25 May 2024
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...
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concrete categories, such as the category of groups or the category of topological spaces. Category of topological spaces Set theory Small set (category theory)...
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although a category may have many distinct skeletons, any two skeletons are isomorphic as categories, so up to isomorphism of categories, the skeleton of a category...
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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...
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popularised by Barry Mitchell (1965)'s influential Theory of categories. Cf. e.g., https://blog.juliosong.com/linguistics/mathematics/category-theory-notes-9/...
6 KB (786 words) - 21:32, 21 September 2023
In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in...
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Morphism (redirect from Morphism (category theory))
In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures...
12 KB (1,499 words) - 19:52, 25 October 2024
Especially for higher categories, the concepts from algebraic topology are also used in the category theory. For that see also glossary of algebraic topology...
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specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms...
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In category theory, two categories C and D are isomorphic if there exist functors F : C → D and G : D → C that are mutually inverse to each other, i.e...
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of the Categories[citation needed]. Ackrill (1963). Thomasson, Amie (2019), Zalta, Edward N. (ed.), "Categories", The Stanford Encyclopedia of Philosophy...
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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...
4 KB (611 words) - 16:26, 28 June 2024