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- Quasi-category abstract "In mathematics, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory. Quasi-categories were introduced by Boardman & Vogt (1973). André Joyal has much advanced the study of quasi-categories showing that most of the usual basic category theory and some of the advanced notions and theorems have their analogues for quasi-categories. An elaborate treatise of the theory of quasi-categories has been expounded by Jacob Lurie (2009).Quasi-categories are certain simplicial sets. Like ordinary categories, they contain objects (the 0-simplices of the simplicial set) and morphisms between these objects (1-simplices). But unlike categories, the composition of two morphisms need not be uniquely defined. All the morphisms that can serve as composition of two given morphisms are related to each other by higher order invertible morphisms (2-simplices thought of as "homotopies"). These higher order morphisms can also be composed, but again the composition is well-defined only up to even higher order invertible morphisms, etc.The idea of higher category theory (at least, higher category theory when higher morphisms are invertible) is that, as opposed to the standard notion of a category, there should be a mapping space (rather than a mapping set) between two objects. This suggests that a higher category should simply be a topologically enriched category. The model of quasi-categories is, however, better suited to applications than that of topologically enriched categories, though it has been proved by Lurie that the two have natural model structures that are Quillen equivalent.".
- Quasi-category wikiPageExternalLink hc2.pdf.
- Quasi-category wikiPageExternalLink Joyal.pdf.
- Quasi-category wikiPageExternalLink InfinityCategories.pdf.
- Quasi-category wikiPageExternalLink The+theory+of+quasi-categories.
- Quasi-category wikiPageID "28662219".
- Quasi-category wikiPageLength "6231".
- Quasi-category wikiPageOutDegree "18".
- Quasi-category wikiPageRevisionID "663941230".
- Quasi-category wikiPageWikiLink André_Joyal.
- Quasi-category wikiPageWikiLink Category:Category_theory.
- Quasi-category wikiPageWikiLink Category_(mathematics).
- Quasi-category wikiPageWikiLink Category_theory.
- Quasi-category wikiPageWikiLink Fundamental_group.
- Quasi-category wikiPageWikiLink Higher_category_theory.
- Quasi-category wikiPageWikiLink Homotopy_category.
- Quasi-category wikiPageWikiLink Kan_complex.
- Quasi-category wikiPageWikiLink Kan_fibration.
- Quasi-category wikiPageWikiLink Nerve_(category_theory).
- Quasi-category wikiPageWikiLink Nerve_of_a_category.
- Quasi-category wikiPageWikiLink Princeton_University_Press.
- Quasi-category wikiPageWikiLink Quillen_adjunction.
- Quasi-category wikiPageWikiLink Simplicial_set.
- Quasi-category wikiPageWikiLink Springer-Verlag.
- Quasi-category wikiPageWikiLink Springer_Science+Business_Media.
- Quasi-category wikiPageWikiLink Stable_infinity_category.
- Quasi-category wikiPageWikiLink Stable_∞-category.
- Quasi-category wikiPageWikiLink Topological_category.
- Quasi-category wikiPageWikiLinkText "Quasi-categories".
- Quasi-category wikiPageWikiLinkText "Quasi-category".
- Quasi-category wikiPageWikiLinkText "quasi categories".
- Quasi-category wikiPageWikiLinkText "quasi-categories".
- Quasi-category wikiPageWikiLinkText "quasi-category".
- Quasi-category wikiPageWikiLinkText "quasicategory".
- Quasi-category wikiPageWikiLinkText "ω-category".
- Quasi-category authorlink "Jacob Lurie".
- Quasi-category first "Jacob".
- Quasi-category hasPhotoCollection Quasi-category.
- Quasi-category last "Lurie".
- Quasi-category wikiPageUsesTemplate Template:Citation.
- Quasi-category wikiPageUsesTemplate Template:Harvs.
- Quasi-category wikiPageUsesTemplate Template:Harvtxt.
- Quasi-category wikiPageUsesTemplate Template:Nlab.
- Quasi-category year "2009".
- Quasi-category subject Category:Category_theory.
- Quasi-category hypernym Generalization.
- Quasi-category type Article.
- Quasi-category type Article.
- Quasi-category type Function.
- Quasi-category comment "In mathematics, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category. The study of such generalizations is known as higher category theory. Quasi-categories were introduced by Boardman & Vogt (1973).".
- Quasi-category label "Quasi-category".
- Quasi-category sameAs Kvazikategorija.
- Quasi-category sameAs m.0czd71x.
- Quasi-category sameAs Q7269442.
- Quasi-category sameAs Q7269442.
- Quasi-category wasDerivedFrom Quasi-category?oldid=663941230.
- Quasi-category isPrimaryTopicOf Quasi-category.