especially (higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology...

to the ordinal number ω. Higher-dimensional categories are part of the broader mathematical field of higher-dimensional algebra, a concept introduced by...

Mathematics portal Higher-dimensional algebra General abstract nonsense Categorification Coherency (homotopy theory) Lurie, Jacob. Higher Topos Theory (PDF)...

if the algebra is of higher dimensionality. One dimensional coordinate systems include the number line. Number line Univariate Zero-dimensional space Гущин...

disk Helicase-dependent amplification High density amorphous ice Higher-dimensional algebra Dragonair Ein Shemer Airfield Hardlines Distribution Alliance...

analogues. Higher category theory Higher-dimensional algebra Categorical ring Crane, Louis; Frenkel, Igor B. (1994-10-01). "Four-dimensional topological...

(in reference to Heyting-algebra higher-dimensional-algebra hyperalgebras Łukasiewicz-Moisil-algebras meta-logics MV-algebras on 2007-07-11) Cited by John...

theorem Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological...

finite-dimensional normed division algebras over the real numbers, while Frobenius theorem states that the first three are the only finite-dimensional associative...

commutative affine algebraic group commonly found in projective algebraic geometry and toric geometry. Higher dimensional algebraic tori can be modelled...

that generalizes structure-preserving maps such as homomorphism between algebraic structures, functions from a set to another set, and continuous functions...

A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because...

and K-Vect, the category of vector spaces over a field. See Zero object (algebra) for details. This is the origin of the term "zero object". In Ring, the...

measure of nonassociativity of Q. In higher-dimensional algebra, where there may be non-identity morphisms between algebraic expressions, an associator is an...

commutative R-algebras is the tensor product. In the category of (noncommutative) R-algebras, the coproduct is a quotient of the tensor algebra (see Free...

algebraic topology. University of Chicago Press, 1999. An introduction to categorical approaches to algebraic topology: the focus is on the algebra,...

to be unique. Pullbacks in differential geometry Equijoin in relational algebra Fiber product of schemes Mitchell, p. 9 Lee, John M. (2003), "Smooth Manifolds"...

[1966]. "Closed categories". Proceedings of the Conference on Categorical Algebra. (La Jolla, 1965. Springer. pp. 421–562. doi:10.1007/978-3-642-99902-4_22...

algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras. Many of the higher-dimensional...

homological algebra. Cambridge University Press. p. 240. Baez, John C.; Crans, Alissa S. (2004). "Higher-dimensional algebra VI: Lie 2-algebras". Theory...

equivalent to the category of commutative Von Neumann algebras (with normal unital homomorphisms of *-algebras). Opposite preserves products: ( C × D ) op ≅ C...

algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures...

topology, and currying, together with apply, provide the adjoint. A Heyting algebra is a Cartesian closed (bounded) lattice. An important example arises from...

Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional conformal...

two-dimensional algebra generated by e1 that squares to −1, and is algebra-isomorphic to C, the field of complex numbers. Cl1,0(R) is a two-dimensional algebra...

n-group, or n-dimensional higher group, is a special kind of n-category that generalises the concept of group to higher-dimensional algebra. Here, n {\displaystyle...

Jaap van Oosten. "Basic category theory" (PDF). Freyd, Peter (1991). "Algebraically complete categories". Proceedings of the International Conference on...

able to explicitly study the structure behind those equalities. Higher-dimensional algebra the study of categorified structures. Hodge theory a method for...

introduced originally as an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogues: the magnitude of...

commutative diagrams play the role in category theory that equations play in algebra. A commutative diagram often consists of three parts: objects (also known...