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Model category

In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations' satisfying certain axioms relating them. These abstract from the category of topological spaces or of chain complexes (derived category theory). The concept was…

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Overview

Motivation

Formal definition

Examples

Some constructions

Characterizations of fibrations and cofibrations by lifting properties

Homotopy and the homotopy category

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Map overview Semantic statistics

Model category

Nodes62
Edges61
Triples49
Avg. degree1.97
Density0.032258
Components1

How this topic connects Entity context

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Model category

Top relations

related to Homotopy and the homotopy category · 10
Model category → Applying, CW, Hovey, However, Model Categories, More, See, The, This, Thm
related to Motivation · 8
Model category → Another, Because, Homology, Homotopy, Model, R-algebras, R-modules, Similarly
related to Topological spaces · 8
Model category → Equivalently, For, Hovey's Model Categories, Hurewicz, Serre, The, This, Top
related to Some constructions · 7
Model category → Analogously, Every, For, Given, If, In, Similarly
related to Formal definition · 6
Model category → Hovey, In, Mark Hovey, Philip Hirschhorn, Quillen, The
is a · 5
Model category → category C and three classes of, category of chain complexes of R-modules for a commutative ring R, category that has a model structure and all, category with distinguished classes of morphisms, simplicial category with a model structure that is compatible with the simplicial structure.Given any category C and a model category M
related to External links · 2
Model category → Joyal's, Model
related to First consequences of the definition · 2
Model category → Also, The
related to Definition via weak factorization systems · 1
Model category → The

Important terminology Word statistics

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Important terminology

model category homotopy fibrations cofibrations categories weak structure equivalences topological spaces simplicial objects given maps classes theory isbn acyclic sets

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Model categoryis acategory with distinguished classes of morphisms0.90text
Model categoryis acategory of chain complexes of R-modules for a commutative ring R0.90text
Model categoryis acategory that has a model structure and all0.90text
Model categoryis acategory C and three classes of0.90text
Model categoryis asimplicial category with a model structure that is compatible with the simplicial structure.Given any category C and a model category M0.90text
Model categoryrelated to Definition via weak factorization systemsThe0.60section
Model categoryrelated to External linksModel0.60section
Model categoryrelated to External linksJoyal's0.60section
Model categoryrelated to First consequences of the definitionThe0.60section
Model categoryrelated to First consequences of the definitionAlso0.60section
Model categoryrelated to Formal definitionThe0.60section
Model categoryrelated to Formal definitionQuillen0.60section

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