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Ind-completion

In mathematics, the ind-completion or ind-construction is the process of freely adding filtered colimits to a given category C. The objects in this ind-completed category, denoted Ind(C), are known as direct systems, they are functors from a small filtered category I to C.

The pro-completion, Basic properties of ind-categories & Definitions

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The pro-completion

Grothendieck (1960)Opposite categoryFinite groupsProfinite groupsPreordered set
17 related topics

Basic properties of ind-categories

CompactCorepresentable functorFinSetCategory of all setsEssentially surjective
6 related topics

Definitions

Natural numbersFinal categoryIdentity morphismPierre Deligne
4 related topics

Infinity-categorical variants

∞-categories
1 related topics

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Overview

Definitions

Basic properties of ind-categories

The pro-completion

Infinity-categorical variants

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Map overview Semantic statistics

Ind-completion

Nodes40
Edges39
Triples13
Avg. degree1.95
Density0.05
Components1

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Ind-completion

Top relations

has application · 4
Ind-completion → Grothendieck's Galois, Pro-completions, Pro-objects, Schlessinger's
related to The pro-completion · 4
Ind-completion → Grothendieck, Like, Pro, The
related to Universal property of the ind-completion · 3
Ind-completion → Ind, The, This
related to Infinity-categorical variants · 2
Ind-completion → Lurie, The

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Important terminology

category filtered ind displaystyle objects direct functor compact colimits object also example equivalent finite pro systems pro-completion equivalence known small

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ind-completionhas applicationPro-completions0.60section
Ind-completionhas applicationPro-objects0.60section
Ind-completionhas applicationGrothendieck's Galois0.60section
Ind-completionhas applicationSchlessinger's0.60section
Ind-completionrelated to Infinity-categorical variantsThe0.60section
Ind-completionrelated to Infinity-categorical variantsLurie0.60section
Ind-completionrelated to The pro-completionLike0.60section
Ind-completionrelated to The pro-completionPro0.60section
Ind-completionrelated to The pro-completionThe0.60section
Ind-completionrelated to The pro-completionGrothendieck0.60section
Ind-completionrelated to Universal property of the ind-completionThe0.60section
Ind-completionrelated to Universal property of the ind-completionInd0.60section

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