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- ...pic on [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] (QAT) introducing ...../PreciseIdea/|concepts]] of QAT based on [[../ModuleAlgebraic/|algebraic topology]] (AT), [[../TrivialGroupoid/|category theory]] (CT) and their [[../NonAbel ...8 KB (1,052 words) - 16:13, 12 September 2020
- ==Algebraic topology== ...for topological spaces. A central problem in algebraic topology is to find algebraic invariants of topological spaces, which is usually carried out by means ...11 KB (1,301 words) - 12:39, 6 May 2023
- ===Category theory concepts in algebraic topology=== .../|non-Abelian categories]] and [[../ModuleAlgebraic/|non-Abelian algebraic topology]] #supplemental axioms for an Abelian category ...7 KB (684 words) - 07:29, 31 October 2023
- ==An Overview of Algebraic Topology topics== ...for topological spaces. A central problem in algebraic topology is to find algebraic invariants of topological spaces, which is usually carried out by means ...3 KB (274 words) - 12:39, 6 May 2023
- ==Algebraic topology topics== ...oduleAlgebraic/|algebraic topology]]'' (AT) utilizes [[../CoIntersections/|algebraic]] approaches to solve [[../CoIntersections/|topological]] problems, ...10 KB (1,003 words) - 12:39, 6 May 2023
- ==Non--Abelian algebraic topology== ...tersections/|algebraic]] treatments of topological invariants in Algebraic Topology. ...3 KB (347 words) - 15:46, 12 September 2020
- ...]] and [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]]. ..../NAQAT2/|nonabelian algebraic topology]] (NAAT)'s generalized approach to topology in terms of [[../GroupoidHomomorphism2/|groupoids]] and [[../CubicalHigherH ...6 KB (711 words) - 12:39, 6 May 2023
- *[[../CubicalHigherHomotopyGroupoid/|algebraic topology]], *[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]], ...65 KB (9,661 words) - 04:57, 12 September 2020
- ==Non-Abelian Quantum Algebraic Topology (NAQAT)== ...ned with the applications of [[../CubicalHigherHomotopyGroupoid/|algebraic topology]] methods, results and constructions (including its extensions to [[../Triv ...4 KB (564 words) - 15:46, 12 September 2020
- Algebraic topology, quantum algebraic topology, n-logic algebraic categories, ...ant to [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]]. A more extensive bibliography on ''[[../TrivialGroupoid/|category theory ...42 KB (6,254 words) - 04:48, 12 September 2020
- *[[../CubicalHigherHomotopyGroupoid/|algebraic topology]], *[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]], ...66 KB (9,854 words) - 12:46, 6 May 2023
- ==topic on the Algebraic Foundations of Quantum Algebraic Topology== ...ons of [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] ([[../QuantumOperatorAlgebra5/|QAT]]) ...10 KB (1,384 words) - 16:14, 12 September 2020
- *[[../ModuleAlgebraic/|algebraic topology]], *[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]], ...66 KB (9,841 words) - 12:46, 6 May 2023
- ==Topical references for Categories and Algebraic Topology Applications in Theoretical Physics== Baianu, I.C.: 1971b, Categories, Functors and Quantum Algebraic ...64 KB (9,619 words) - 14:11, 6 May 2023
Page text matches
- ==An Overview of Algebraic Topology topics== ...for topological spaces. A central problem in algebraic topology is to find algebraic invariants of topological spaces, which is usually carried out by means ...3 KB (274 words) - 12:39, 6 May 2023
- ==Non--Abelian algebraic topology== ...tersections/|algebraic]] treatments of topological invariants in Algebraic Topology. ...3 KB (347 words) - 15:46, 12 September 2020
- #Cohomology in [[../AbelianCategory3/|noncommutative]] [[../CoIntersections/|algebraic]] geometry Hatcher, A. 2001. [http://www.math.cornell.edu/~hatcher/AT/AT.pdf ''Algebraic Topology'' (textbook on line).], Cambridge University Press; Cambridge, UK., 405 pa ...2 KB (293 words) - 16:14, 12 September 2020
- ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...1 KB (163 words) - 04:51, 12 September 2020
- ...]] and [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]]. ...gy]] ([[../NonabelianAlgebraicTopology3/|NAAT]])'s generalized approach to topology in terms of [[../GroupoidHomomorphism2/|groupoids]] and [[../CubicalHigherH ...3 KB (383 words) - 15:47, 12 September 2020
- ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...1 KB (184 words) - 21:39, 6 March 2022
- ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...1 KB (206 words) - 04:50, 12 September 2020
- Hausdorff topology, that is, if given any distinct points <math>x,y\in X_{LC}</math>, there ex ...ebra5/|QAT]]), topological QFT ([[../SUSY2/|TQFT]]), [[../CoIntersections/|algebraic]] QFT ([[../SUSY2/|AQFT]]), [[../PureState/|axiomatic QFT]], [[../QuantumCo ...2 KB (290 words) - 04:40, 1 July 2015
- ...a [[../Triangulation Methods For Quantized Spacetimes 2|Quantum Algebraic Topology]] [[../Trivial Groupoid|object]], a ''[[../LQG2|quantum automaton]]'' is de is defined as an ''algebraic category'' [[../Category Of Logic Algebras|category of logic algebras]] who ...3 KB (424 words) - 20:08, 9 September 2020
- ==Algebraic topology topics== ...oduleAlgebraic/|algebraic topology]]'' (AT) utilizes [[../CoIntersections/|algebraic]] approaches to solve [[../CoIntersections/|topological]] problems, ...10 KB (1,003 words) - 12:39, 6 May 2023
- ...topology, and especially in [[../CubicalHigherHomotopyGroupoid/|algebraic topology]]; they may be considered as one of the simplest, special [[../Bijective/|t ...'' -- concepts in algebraic topology (<ref name='BR2006'>R. Brown. 2006. ''Topology and Groupoids'' . Booksurge PLC.</ref>) ...5 KB (656 words) - 23:58, 30 August 2020
- ...pplicationsInTheoreticalPhysics/|Bibliography for categories and algebraic topology]] ...578 bytes (66 words) - 04:51, 12 September 2020
- #[[../ModuleAlgebraic/|non-Abelian algebraic topology]], including also non-Abelian homological algebra; [http://www.bangor.ac.uk/~mas010/nonab-a-t.html non-Abelian algebraic topology overview] and ...4 KB (530 words) - 15:46, 12 September 2020
- ===Non-commutative Geometry and Non-Abelian Algebraic Topology=== ...commutative]] 'spaces' (in fact ''non-commutative'' [[../TrivialGroupoid/|algebraic structures]], or algebras of [[../Bijective/|functions]]). ...3 KB (399 words) - 15:46, 12 September 2020
- ==Non-Abelian Quantum Algebraic Topology (NAQAT)== ...ned with the applications of [[../CubicalHigherHomotopyGroupoid/|algebraic topology]] methods, results and constructions (including its extensions to [[../Triv ...4 KB (564 words) - 15:46, 12 September 2020
- ...commutative]]) are relevant to [[../ModuleAlgebraic/|non-Abelian algebraic topology]] ([[../NAQAT2/|NAAT]]) and [http://planetphysics.org/?op=getobj&from=lec&i ...t allow generalizations of important [[../Formula/|theorems]] in algebraic topology and higher dimensional algebra, such as the [[../SingularComplexOfASpace/|g ...2 KB (277 words) - 15:45, 12 September 2020
- ...commutative]]) are relevant to [[../ModuleAlgebraic/|non-Abelian algebraic topology]] ([[../NAQAT2/|NAAT]]) and [http://planetphysics.org/?op=getobj&from=lec&i ...t allow generalizations of important [[../Formula/|theorems]] in algebraic topology and higher dimensional algebra, such as the [[../SingularComplexOfASpace/|g ...2 KB (277 words) - 15:45, 12 September 2020
- ...gebroid/|quantum algebroid]] or a higher dimensional [[../TrivialGroupoid/|algebraic structure]] (as previously defined in [[../HigherDimensionalAlgebra2/|highe ...y as a [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] [[../TrivialGroupoid/|object]] determined by the ''quantum triplet'' <ma ...2 KB (208 words) - 15:56, 12 September 2020
- ...]] and [[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]]. ..../NAQAT2/|nonabelian algebraic topology]] (NAAT)'s generalized approach to topology in terms of [[../GroupoidHomomorphism2/|groupoids]] and [[../CubicalHigherH ...6 KB (711 words) - 12:39, 6 May 2023
- ...ory]] #[[../TriangulationMethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] (QAT) #Bibliography for mathematical physics and quantum algebraic topology ...5 KB (444 words) - 14:10, 6 May 2023