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...

around another DNA element, a functional region of DNA, including genes and cis-regulatory elements. Element (category theory) Element (mathematics), one...

In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category...

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...

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...

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

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Writing A = { 1 , 2 , 3 , 4 } {\displaystyle...

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...

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

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

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

{\mbox{Hom}}(A,B)} either has one element or is empty, has a partially ordered set as a skeleton. Glossary of category theory Thin category Adámek, Jiří, Herrlich...

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

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

generally, in category theory, the morphisms of an object to itself form a monoid, and, conversely, a monoid may be viewed as a category with a single...

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...

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

operation is associative and has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed...

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 mathematics, specifically in category theory, an F {\displaystyle F} -coalgebra is a structure defined according to a functor F {\displaystyle F} ...

In mathematics, specifically category theory, a family of generators (or family of separators) of a category C {\displaystyle {\mathcal {C}}} is a collection...

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

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

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

a definite choice of an element from each set, and makes it unnecessary to add the axiom of choice to our axioms of set theory. The difficulty appears...

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...

any particular one-element set serving as the unit. Cat, the category of small categories with the product category, where the category with one object and...