a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T. Initial objects are...

described more concisely as initial and terminal objects in a comma category (i.e. one where morphisms are seen as objects in their own right). Let F :...

0o, or zero object, a mathematics term for a simultaneously initial and terminal object 0O, also ZO, an abbreviation for zero order Zero-order hold,...

any other zeros are considered to be non-trivial. Degeneracy Initial and terminal objects List of mathematical jargon Pathological Trivialism Trivial measure...

supremum and essential infimum Initial and terminal objects Maximal and minimal elements Limit superior and limit inferior (infimum limit) Upper and lower...

Category of magmas Initial object Terminal object Zero object Subobject Group object Magma object Natural number object Exponential object Epimorphism Monomorphism...

with a terminal object 1 and binary coproducts (denoted by +), an NNO can be defined as the initial algebra of the endofunctor that acts on objects by X...

absorbing element, and whose principal ideal is the smallest ideal. A zero object in a category is both an initial and terminal object (and so an identity...

colimits. The zero ring serves as both an initial and terminal object in Rng (that is, it is a zero object). It follows that Rng, like Grp but unlike...

three properties: It has a terminal object. Any two objects X and Y of C have a product X ×Y in C. Any two objects Y and Z of C have an exponential ZY...

category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category. The fibrant objects of a closed model category...

"glue together" several related objects, the precise gluing process being specified by morphisms between the objects. Thus, inverse limits can be defined...

groups or rings, and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism...

The Bloomberg Terminal is a computer software system provided by the financial data vendor Bloomberg L.P. that enables professionals in the financial service...

{\displaystyle C} be a category and let X 1 {\displaystyle X_{1}} and X 2 {\displaystyle X_{2}} be objects of C . {\displaystyle C.} An object is called the coproduct...

by +), and binary products (denoted by ×), a list object over A can be defined as the initial algebra of the endofunctor that acts on objects by X ↦ 1...

where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to...

2-morphisms. The initial object of Cat is the empty category 0, which is the category of no objects and no morphisms. The terminal object is the terminal category...

In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. This initiality provides a general framework...

construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector...

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

category C is a category S whose objects are objects in C and whose morphisms are morphisms in C with the same identities and composition of morphisms. Intuitively...

xy = 0 for all x and y. This article refers to the one-element ring.) In the category of rings, the zero ring is the terminal object, whereas the ring...

following we will consider the limit (L, φ) of a diagram F : J → C. Terminal objects. If J is the empty category there is only one diagram of shape J: the...

composition. Morphisms and objects are constituents of a category. Morphisms, also called maps or arrows, relate two objects called the source and the target of...

embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category. It is an important...

every object X {\displaystyle X} in C {\displaystyle C} , a morphism η X : F ( X ) → G ( X ) {\displaystyle \eta _{X}:F(X)\to G(X)} between objects of D...

language with objects and morphisms as distinct sorts, together with the relations of an object being the source or target of a morphism and a symbol for...

objects X and Y and two parallel morphisms f, g : X → Y. More explicitly, a coequalizer of the parallel morphisms f and g can be defined as an object...

For each object Y in D, choose an initial morphism (f(Y), ηY) from Y to G, so that ηY : Y → G(f(Y)). We have the map of f on objects and the family...