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 :...

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...

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

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,...

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...

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...

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...

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...

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

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...

represented by certain decorated framed tangle diagrams, where the initial and terminal objects are represented by the boundary components of the tangle. In...

the absence of other forces, objects and people will experience weightlessness in these situations. Examples of objects not in free-fall: Flying in an...

called Cartesian closed if and only if it satisfies the following three properties: It has a terminal object. Any two objects X and Y of C have a product X ×Y...

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...

model category has a terminal object by completeness and an initial object by cocompleteness, since these objects are the limit and colimit, respectively...

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...

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

{\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...

will be both terminal (a nullary product) and initial (a nullary coproduct), it will in fact be a zero object. Indeed, the term "zero object" originated...

objects are lists (finite sequences) A1, ..., An of objects of C; there are arrows between two objects A1, ..., Am and B1, ..., Bn only if m = n, and...

product, i.e., a final object) is necessarily a coproduct (or initial object in the case of an empty diagram), and hence a biproduct, and conversely every finitary...

≈9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law. In short, terminal velocity...

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...

to coproducts and coequalizers (if there is an initial object) in the sense that: Coproducts are a pushout from the initial object, and the coequalizer...

object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects...

factorization is possible for every cone. Limits may also be characterized as terminal objects in the category of cones to F. It is possible that a diagram does not...