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- ==Theory of Categories== ''Category theory'' can be described as the branch of mathematics concerned ...10 KB (1,393 words) - 04:57, 12 September 2020
- ==Enriched Category Theory== ...a new, contributed topic on enrichments of [[../TrivialGroupoid/|category theory]], including a weak [[../AbelianCategoryEquivalenceLemma/|Yoneda lemma]], [ ...2 KB (256 words) - 05:12, 12 September 2020
- ==Index of Category Theory== #[[../TrivialGroupoid/|category theory]] #[[../TrivialGroupoid/|object]] #[[../Cod/|identity]] #arrow ...5 KB (480 words) - 06:19, 11 October 2023
- If you've done a bit of group theory (if you haven't, you should, but for the moment you can just ignore this pa [[Category:Category theory]] ...15 KB (2,571 words) - 16:21, 8 September 2020
- A ''category'' <math>\mathcal{C}</math> consists of the following data: ...ition' already introduced in the discussion of [[Introduction to Category Theory/Sets_and_Functions#Functions | functions]]. So we're making a shift from t ...30 KB (5,156 words) - 12:45, 11 March 2023
- ...'''. A (covariant) functor ''F'' from category <math>\mathcal{C}</math> to category <math>\mathcal{D}</math> satisfies [[Category:Category theory]] ...3 KB (456 words) - 16:00, 19 April 2023
- [[Category:Category theory]] ...318 bytes (39 words) - 18:56, 11 December 2009
- ...ts, functions, and function composition. In fact, sets and functions are a category called Sets. ...'t define 'small' or 'large' here, it's left for an advanced course in set theory.</ref> ...15 KB (2,523 words) - 01:36, 9 May 2021
- One of the features of category theory is how it unifies very disparate phenomena. The product construction compr * If <math>X</math> is any object in the category, and <math>f_1: X \to A</math> and <math>f_2: X \to B</math> are any morphi ...33 KB (5,702 words) - 11:19, 24 September 2019
- [[image:Cone category 2obj.svg|frame|right|Cone category over (C1, C2).]] ...e any two objects in category <math>\mathcal{C}</math>. We define the cone category, <math>\mathcal{C}one(C_1, C_2)</math>, as follows ...30 KB (5,265 words) - 15:59, 19 April 2023
- One of the most simple constructions in category theory is product. In this lesson we first define the product and coproduct of set ...dered set''' or '''poset'''. We will later see that poset is an example of category, where arrows are not functions. ...11 KB (1,757 words) - 10:04, 9 July 2023
- ...bstract and applied mathematics. A more extensive bibliography on category theory can be found on the [http://plato.stanford.edu/entries/category-theory/ Plato, Stanford Encyclopedia of Philosophy web site]. ...66 KB (9,841 words) - 12:46, 6 May 2023
- Awodey, S., 2004, An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism., ''Philosophia Mathemat Awodey, S., 2006, ''Category Theory'' , Oxford: Clarendon Press. ...64 KB (9,619 words) - 14:11, 6 May 2023
Page text matches
- ...Euler-Bernoulli beam theory <math>C^1</math>? Why is the Timoshenko beam theory <math>C^0</math>?}} In the Euler-Bernoulli theory, the rate of deformation in the <math>xx</math> direction is given by ...879 bytes (139 words) - 04:31, 3 June 2018
- #[[../CubicalHigherHomotopyGroupoid/|homotopy theory]] and [[../Pushout/|fundamental groups]] #Topology and [[../GroupoidHomomor #[[../CategoricalOntology/|category theory applications]] in algebraic topology ...3 KB (274 words) - 12:39, 6 May 2023
- ...ilinear form]] ([[w:Cartan-Killing form]]) and is pivotal in the structure theory of representations of Lie algebras. *James Humphreys: ''Introduction to Lie algebras and representation theory'', {{ISBN|9780387900537}} , pp.27,118 ...969 bytes (135 words) - 03:38, 1 May 2017
- ...]] of the basis elements. This theorem is fundamental in [[representation theory]]. It gives an concrete description of <math>U(\mathfrak{g})</math>; And, *James. E. Humphreys, ''Introduction to Lie algebras and representation theory'', pp.91-93 (detailed) ...1 KB (135 words) - 18:34, 16 November 2014
- ...f orientation-preserving diffeomorphisms of the circle. The representation theory of Virasoro algebra is rich, and has diverse applications in Mathematics an ==Representation Theory== ...2 KB (251 words) - 23:03, 26 July 2017
- ...tor'' introduced for example in [[../AbelianCategory2/|abelian category]] theory. #Category of diagrams and 2-functors ...2 KB (177 words) - 04:55, 12 September 2020
- ...Undergraduate/Pure Mathematics|School of Mathematics:Introduction to Graph Theory}} [[School of Mathematics:Introduction to Graph Theory:Proof of Theorem 2|Theorem 2]]: A graph is a forest if and only if for ever ...2 KB (376 words) - 13:10, 14 October 2016
- ...Undergraduate/Pure Mathematics|School of Mathematics:Introduction to Graph Theory}} [[School of Mathematics:Introduction to Graph Theory:Proof of Corollary 3|Corollary 3]]: A graph is a tree if and only if for ev ...4 KB (760 words) - 03:10, 12 January 2016
- ...or biosystems in terms of a network, [[../Bijective/|graph]] or [[../Cod/|category]] of integrated interactions between their structural and functional compon ...of items (objects--in the mathematical sense) by means of the mathematical theory of categories into three levels of [[../GenericityInOpenSystems/|dynamic sy ...4 KB (438 words) - 14:12, 6 May 2023
- #[[../SR/|general relativity]] Theory #Axiomatic and Algebraic Quantum Field Theory ...4 KB (507 words) - 04:44, 12 September 2020
- :*[[w:Kinetic theory|Kinetic theory]] (advanced discussion of the ''ideal gas law'') [[Category:Engineering thermodynamics]] ...1 KB (171 words) - 17:44, 21 March 2015
- ...ve reasoning (meaning, if constructed properly, cannot be wrong) whereas a theory in the sciences is inductive reasoning (meaning it's probably correct, but [[Category:Mathematical proofs]] ...2 KB (275 words) - 03:50, 16 October 2014
- ...math>--spectrum one is able to canonically define an associated cohomology theory; thus, one defines the cohomology groups of a CW-complex <math>K</math> ass ...lexes and basepoint preserving maps; furthermore, every reduced cohomology theory on CW complexes arises in this manner from an <math>\Omega</math>-spectrum ...4 KB (676 words) - 15:47, 12 September 2020
- ...operator product expansion]] of [[w:Conformal field theory|conformal field theory]] is analogous to the product of functions over a manifold in [[w:Harmonic In certain limits of [[w:two-dimensional conformal field theory|two-dimensional CFTs]], correlation functions reduce to integrals over fini ...4 KB (611 words) - 21:51, 4 December 2021
- ...math>--spectrum one is able to canonically define an associated cohomology theory; thus, one defines the cohomology groups of a CW-complex <math>K</math> ass ...furthermore, every reduced [[../CohomologyTheoryOnCWComplexes/|cohomology theory on CW complexes]] arises in this manner from an <math>\Omega</math>-spectru ...4 KB (677 words) - 21:45, 6 March 2022
- == Liouville theory and non-diagonal minimal models == === Liouville theory === ...3 KB (452 words) - 16:57, 10 March 2025
- {{nav3|Wikiversity|Wikiversity:School of Computer Science|Wikiversity:Theory}} ...es of language families defined in a wide variety of ways. Formal language theory is concerned with the purely syntactical aspects, rather than a semantics o ...5 KB (809 words) - 14:34, 1 July 2017
- ...ville field theory|Liouville theory]] is an interesting 2d conformal field theory, which has been solved in the sense that 3pt structure constants are exactl The theory is also quite well understood in the presence of a boundary, with boundary ...4 KB (606 words) - 11:36, 30 October 2024
- theory. #[[../CubicalHigherHomotopyGroupoid/|homotopy theory]] and [[../HomotopyCategory/|fundamental groups]] #Topology and [[../Quantu ...10 KB (1,003 words) - 12:39, 6 May 2023
- ...eorem in [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum field theory]]) ...G. Emch, "Algebraic methods in statistical mechanics and quantum field theory." , Wiley (1972) ...2 KB (295 words) - 06:20, 11 October 2023