• the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being...
    34 KB (4,737 words) - 12:26, 19 September 2024
  • Thumbnail for Category theory
    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
  • (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 and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms, the kernels...
    7 KB (950 words) - 06:26, 1 October 2023
  • higher category theory, the concept of higher categorical structures, such as (∞-categories), allows for a more robust treatment of homotopy theory, enabling...
    9 KB (944 words) - 09:25, 24 April 2024
  • Thumbnail for Category (mathematics)
    of categories, and doing so often reveals deep insights and similarities between seemingly different areas of mathematics. As such, category theory provides...
    21 KB (2,525 words) - 15:16, 17 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
  • Conferences: Applied category theory Symposium on Compositional Structures (SYCO) Books: Picturing Quantum Processes Categories for Quantum Theory An Invitation...
    7 KB (670 words) - 10:24, 16 September 2024
  • Thumbnail for Monoid (category theory)
    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...
    5 KB (511 words) - 14:20, 31 January 2024
  • 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, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas...
    14 KB (2,379 words) - 17:32, 11 September 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...
    5 KB (713 words) - 00:15, 6 March 2024
  • use of categories. Category Functor Natural transformation Homological algebra Diagram chasing Topos theory Enriched category theory Higher category theory...
    5 KB (402 words) - 15:20, 29 March 2024
  • 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
  • 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
  • Thumbnail for Section (category theory)
    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 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...
    10 KB (1,724 words) - 18:43, 7 November 2022
  • 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
  • concrete categories, such as the category of groups or the category of topological spaces. Category of topological spaces Set theory Small set (category theory)...
    9 KB (1,172 words) - 14:28, 4 July 2024
  • 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...
    7 KB (1,148 words) - 17:06, 4 September 2024
  • 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...
    9 KB (1,214 words) - 22:03, 31 July 2024
  • specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms...
    3 KB (268 words) - 11:52, 31 October 2021
  • 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...
    4 KB (460 words) - 07:49, 2 February 2024
  • 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
  • of the Categories[citation needed]. Ackrill (1963). Thomasson, Amie (2019), Zalta, Edward N. (ed.), "Categories", The Stanford Encyclopedia of Philosophy...
    13 KB (1,645 words) - 05:24, 27 October 2024
  • 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...
    5 KB (758 words) - 09:58, 16 January 2024
  • prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are...
    19 KB (2,643 words) - 03:45, 26 March 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...
    6 KB (924 words) - 07:40, 5 March 2024
  • 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