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...

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 mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing...

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, duality is a correspondence between the properties of a category C and the dual properties of the opposite...

and normalizer Center (category theory) Kilp, Mati; Knauer, Ulrich; Mikhalev, Aleksandr V. (2000). Monoids, Acts and Categories. De Gruyter Expositions...

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

constituents in general category theory Element (mathematics), one of the constituents of set theory in mathematics Differential element, an infinitesimally...

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 mathematics, the Elementary Theory of the Category of Sets or ETCS is a set of axioms for set theory proposed by William Lawvere in 1964. Although it...

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

In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely...

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...

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, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is...

background to the mathematical idea of topos. This is an aspect of category theory, and has a reputation for being abstruse. The level of abstraction...

In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms...

of the Swiss alchemist Paracelsus. He reasoned that Aristotle's four element theory appeared in bodies as three principles. Paracelsus saw these principles...

third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of...

generally, an element of some abstract topological space Point, or Element (category theory), generalizes the set-theoretic concept of an element of a set...

between category theory and monoids see below. The set of homeomorphism classes of compact surfaces with the connected sum. Its unit element is the class...

In category theory, a branch of mathematics, a presheaf on a category C {\displaystyle C} is a functor F : C o p → S e t {\displaystyle F\colon C^{\mathrm...

general is in category theory. The algebraic objects to which representation theory applies can be viewed as particular kinds of categories, and the representations...

it is surjective. In category theory, right inverses are also called sections, and left inverses are called retractions. An element is invertible under...

Within the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself. This implies that a singleton...

In category theory, a branch of mathematics, profunctors are a generalization of relations and also of bimodules. A profunctor (also named distributor...

Glossary of category theory Thin category Adámek, Jiří, Herrlich, Horst, & Strecker, George E. (1990). Abstract and Concrete Categories. Originally published...

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

In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of...