Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer...

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

Categorical logic Applied category theory Category of sets Concrete category Category of vector spaces Category of graded vector spaces Category of chain complexes...

introductory texts on category theory and its applications, Category Theory for the Sciences and An Invitation to Applied Category Theory. Spivak received...

behind those equalities. Higher category theory is often applied in algebraic topology (especially in homotopy theory), where one studies algebraic invariants...

foams in loop quantum gravity, applications of higher categories to physics, and applied category theory. Additionally, Baez is known on the World Wide Web...

category theory, a branch of mathematics, a monad is a triple ( T , η , μ ) {\displaystyle (T,\eta ,\mu )} consisting of a functor T from a category to...

In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well-behaved type of morphism...

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...

relate various categories. Thus, functors are important in all areas within mathematics to which category theory is applied. The words category and functor...

An Invitation to Applied Category Theory". arXiv:1803.05316 [math.CT]. Joyal, André; Street, Ross (1993). "Braided Tensor Categories" (PDF). Advances...

In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat...

abstract theories. For instance, representing a group by an infinite-dimensional Hilbert space allows methods of analysis to be applied to the theory of groups...

In linguistics, X-bar theory is a model of phrase structure and a theory of syntactic category formation that proposes a universal schema for how phrases...

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...

In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of...

Prototype theory has also been applied in linguistics, as part of the mapping from phonological structure to semantics. In formulating prototype theory, Rosch...

In the mathematical field of category theory, the category of sets, denoted by Set, is the category whose objects are sets. The arrows or morphisms between...

In category theory, a branch of mathematics, a symmetric monoidal category is a monoidal category (i.e. a category in which a "tensor product" ⊗ {\displaystyle...

engineering and medicine. Applied science is often contrasted with basic science, which is focused on advancing scientific theories and laws that explain...

the sense used in category theory, but not in the sense used by Hausmann and Ore. Nevertheless, influential books in semigroup theory, including Clifford...

Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed...

in the framework of one-universe foundation for category theory, the term conglomerate is applied to arbitrary sets as a contraposition to the distinguished...

In category theory, a branch of mathematics, there are several ways (completions) to enlarge a given category in a way somehow analogous to a completion...

In algebraic K-theory, the K-theory of a category C (usually equipped with some kind of additional data) is a sequence of abelian groups Ki(C) associated...

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...

In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories...

Grounded theory is a systematic methodology that has been largely applied to qualitative research conducted by social scientists. The methodology involves...

In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified...

In category theory, a branch of mathematics, the opposite category or dual category C op {\displaystyle C^{\text{op}}} of a given category C {\displaystyle...