a zero object. A strict initial object I is one for which every morphism into I is an isomorphism. The empty set is the unique initial object in Set,...

In the mathematical discipline of category theory, a strict initial object is an initial object 0 of a category C with the property that every morphism...

space is the unique initial object in the category of topological spaces with continuous maps. In fact, it is a strict initial object: only the empty set...

coproducts is monoidal with the coproduct as the monoidal product and the initial object as the unit. Such a monoidal category is called cocartesian monoidal...

serializability. A transaction is holding a lock on an object if that transaction has acquired a lock on that object which has not yet been released. For 2PL, the...

In object-oriented (OO) and functional programming, an immutable object (unchangeable object) is an object whose state cannot be modified after it is...

concept is too strict for some purposes in for example, homotopy theory, where "weak" structures arise in the form of higher categories, strict cubical higher...

Universal morphisms can also be thought more abstractly as initial or terminal objects of a comma category (see § Connection with comma categories,...

2-morphism is a natural transformation between functors. The concept of a strict 2-category was first introduced by Charles Ehresmann in his work on enriched...

focuses on strict 2-groups. A strict 2-group is a strict monoidal category in which every morphism is invertible and every object has a strict inverse (so...

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...

also called strict partial orders. Strict and non-strict partial orders can be put into a one-to-one correspondence, so for every strict partial order...

The strict 2-group is the group object in the category of small categories. Given a category C with finite coproducts, a cogroup object is an object G of...

satisfied: If the transaction T i {\displaystyle T_{i}} in S1 reads an initial value for object X, so does the same transaction T i {\displaystyle T_{i}} in S2...

{\displaystyle a<a} by asymmetry. This definition resembles that of an initial object of a category, but is weaker. Roland Fraïssé (December 2000). Theory...

and non-rigid) and head-initial types. The identification of headedness is based on the following: the order of subject, object, and verb the relationship...

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

numbers object (NNO) is an object endowed with a recursive structure similar to natural numbers. More precisely, in a category E with a terminal object 1,...

typically starts from one, so it assigns to each object the size of the initial segment with that object as last element. Note that these numbers are one...

injective object. 2.  The term “projective limit” is another name for an inverse limit. PROP A PROP is a symmetric strict monoidal category whose objects are...

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...

and coequalizers (if there is an initial object) in the sense that: Coproducts are a pushout from the initial object, and the coequalizer of f, g : X...

category is formed by two sorts of objects: the objects of the category, and the morphisms, which relate two objects called the source and the target of...

In linguistic typology, a verb–object–subject or verb–object–agent language, which is commonly abbreviated VOS or VOA, is one in which most sentences...

on the basis of the Object 220, in the form of the Object 221 (with an 85 mm gun), Object 222 (with the F-32 76.2 mm gun) and Object 223 (built to develop...

vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is...

the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions. Category...

In syntax, verb-initial (V1) word order is a word order in which the verb appears before the subject and the object. In the more narrow sense, this term...

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isomorphism Φ : homC(f−,−) → homD(−,G−). For each object X in C, each object Y in D, as (f(Y), ηY) is an initial morphism, then ΦY, X is a bijection, where ΦY...