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Limit (category theory)

In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits.

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Overview

Definition

Limits

Colimits

Examples

Properties

Functors and limits

A note on terminology

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Map overview Semantic statistics

Limit (category theory)

Nodes90
Edges89
Triples12
Avg. degree1.98
Density0.022222
Components1

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Important terminology Word statistics

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Important terminology

limits diagram functor limit category colimits morphisms one small displaystyle cone shape isomorphism morphism universal object every set objects natural

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
productsinstance ofthe abstract notion of a limit captures the essential properties of universal constructions0.80text
pullbacksinstance ofthe abstract notion of a limit captures the essential properties of universal constructions0.80text
inverse limitsinstance ofthe abstract notion of a limit captures the essential properties of universal constructions0.80text
disjoint unionsinstance ofThe dual notion of a colimit generalizes constructions0.80text
direct sumsinstance ofThe dual notion of a colimit generalizes constructions0.80text
coproductsinstance ofThe dual notion of a colimit generalizes constructions0.80text
pushoutsinstance ofThe dual notion of a colimit generalizes constructions0.80text
direct limits.Limitsinstance ofThe dual notion of a colimit generalizes constructions0.80text
colimitsinstance ofThe dual notion of a colimit generalizes constructions0.80text
like the strongly related notions of universal propertiesinstance ofThe dual notion of a colimit generalizes constructions0.80text
adjoint functorsinstance ofThe dual notion of a colimit generalizes constructions0.80text
exist at a high level of abstractioninstance ofThe dual notion of a colimit generalizes constructions0.80text

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