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...

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

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, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit...

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...

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

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...

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

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

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

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...

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

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...

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 an...

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 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...

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

specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory. Categories with all...

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 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...

theory, infinitary Lawvere theory, and finite-product theory. Algebraic theory Clone (algebra) Monad (category theory) Lawvere theory at the nLab Hyland, Martin;...

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

In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general...

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal...

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...

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...

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...