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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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

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...

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...

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...

the morphisms f {\displaystyle f} and g {\displaystyle g} consists of an object P {\displaystyle P} and two morphisms p 1 : P → X {\displaystyle p_{1}:P\rightarrow...

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...

an object is constructed from a class via instantiation. Memory is allocated and initialized for the object state and a reference to the object is provided...

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...

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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...

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...

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,...

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...

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...

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...