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'''Object theory''' can refer to *The object of a [[metatheory]]. ...

{{wiktionary|object|object-oriented}} '''Object''' may refer to: ...

*In group theory, an element of a [[free abelian group]], a sum of finitely many elements fr ...nce of numbers or other quantities, considered as an abstract mathematical object regardless of whether the sum converges. ...

{{Short description|1=Overview of and topical guide to category theory}} ...as of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be ...

In [[Abstract algebra|algebra]], the '''coimage''' of a [[homomorphism]] ...''coimage''' of a [[morphism]] is the dual notion of the [[image (category theory)|image of a morphism]]. If <math>f : X \rightarrow Y</math>, then a coimag ...

...objects called [[Graph (discrete mathematics)|graphs]] studied in [[graph theory]]. ...puter science)|instances]]. [[Object diagram]]s are subsets of the overall object graph. ...

...Abstract (summary)#Structure}}In [[mathematics]] and related fields, an '''abstract structure''' is a way of describing a set of mathematical objects and the r ...or ''implement'' an abstract structure, the structure itself exists as an abstract concept, independent of any particular representation. ...

...]]. Outside that field, it has been influential particularly on [[category theory]] and [[categorical logic]]. In the usual formulation, the point of view treats not [[object (category theory)|objects]] ''X'' of a given category ''C'', but [[morphism]]s ...

[[Order theory]] is a branch of [[mathematics]] that studies various kinds of objects (oft ...habetical list of many notions of order theory can be found in the [[order theory glossary]]. See also [[inequality (mathematics)|inequality]], [[extreme val ...

...tegory theory|the concept in cognitive psychology and philosophy|prototype theory}} ...s can be thought of as categories with a single [[object (category theory)|object]]. A monoid-graded or group-graded category is therefore one in which to ea ...

...art'', that of abstract knowledge, was deemed an important art educational theory.<ref>MacDonald, Stuart. ''The History and Philosophy of Art Education''. Ja ...

...by [[Paul Dirac]] in his early formulation of [[Quantum mechanics|quantum theory]], from around 1927.<ref>{{cite journal |last=Dirac |first=P. A. M. |title= ...ns in [[quantum mechanics]] may thus be viewed as the systematic theory of abstract, generalized rotations in this space of [[quantum state]] vectors. ...

...l category''' or '''nonempty finite ordinal category''') is the [[category theory|category]] of [[Empty set|non-empty]] finite [[ordinal number|ordinals]] an ...t with the codomain category being the category of sets. A '''cosimplicial object''' is defined similarly as a covariant functor originating from <math>\Delt ...

A simplicial manifold is a [[simplicial complex]] for which the [[Abstract simplicial complex|geometric realization]] is [[homeomorphic]] to a [[topol ==A simplicial object built from manifolds== ...

{{distinguish|Abstract data type}} ...'concrete type''' {{em|can}} be instantiated directly. Instantiation of an abstract type can occur only indirectly, via a concrete [[Subtyping|''subtype'']]. ...

{{Short description|Philosophical theory}} ...contains some objects, there is at least one that contains only [[abstract object]]s.<ref>{{cite journal | last=Cameron | first=Ross P. | title=Much Ado Abou ...

...J'' is [[small category|small]]) has a limit in ''C''. [[Duality (category theory)|Dually]], a '''cocomplete category''' is one in which all small [[colimit] ...category]]: for any two objects there can be at most one morphism from one object to the other. ...

...f entirely new mathematical disciplines, such as [[statistics]] and [[game theory]]. Mathematicians also engage in [[pure mathematics]], or mathematics for i ...

{{Short description|Mathematical object in category theory}} ...del category|model categories]]. The dual notion is that of a [[projective object]]. ...

* [[Normalization process theory]], a sociological theory of the implementation of new technologies or innovations ...lizing (abstract rewriting)]], an abstract rewriting system in which every object has at least one normal form ...