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...

the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept...

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products...

categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer science also rely on category theory,...

functor Hom functor Product (category theory) Equaliser (mathematics) Kernel (category theory) Pullback (category theory)/fiber product Inverse limit Pro-finite...

monoidal category Product (category theory), a generalization of mathematical products Fibre product or pullback Coproduct or pushout Wick product of random variables...

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

But also, in category theory, one has: the fiber product or pullback, the product category, a category that is the product of categories. the ultraproduct...

In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows...

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...

object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category theory is a branch of mathematics that...

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...

ordinary tensor product makes vector spaces, abelian groups, R-modules, or R-algebras into monoidal categories. Monoidal categories can be seen as a...

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...

In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in...

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

a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.) Notes on foundations: In many expositions...

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...

morphisms. As such, it is a concrete category. The study of this category is known as group theory. There are two forgetful functors from Grp, M: Grp → Mon from...

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...

In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any...

type theory, a product of types is another, compounded, type in a structure. The "operands" of the product are types, and the structure of a product type...

In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces...

generators). The free product is the coproduct in the category of groups. That is, the free product plays the same role in group theory that disjoint union...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

In category theory, an end of a functor S : C o p × C → X {\displaystyle S:\mathbf {C} ^{\mathrm {op} }\times \mathbf {C} \to \mathbf {X} } is a universal...

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

smash product as a kind of tensor product in an appropriate category of pointed spaces. Adjoint functors make the analogy between the tensor product and...

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...

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