In higher category theory in mathematics, a Cisinski model structure is a special kind of model structure on topoi. In homotopical algebra, the category...
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is again a weak categorical equivalence. The Joyal model structure is a Cisinski model structure and in particular cofibrantly generated. Cofibrations...
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geometry. In 2001, Cisinski model structures on topoi were introduced and later named after him. Since 2016, Denis-Charles Cisinski works at the Universität...
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A.2.3.2. Cisinski 2019, Corollary 3.1.10. Lurie 2009, Higher Topos Theory, Theorem 1.3.4.1. Cisinski 2019, Proposition 3.8.3. model structure on simplicial...
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2009, Notation 2.2.3.8. Cisinski 2019, 4.4.8. & 4.4.19. Cisinski 2019, Eq. (4.4.21.2) Cisinski 2019, Eq (4.4.19.1) Cisinski 2019, Proposition 4.4.6....
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localization of the model category of simplicial presheaves. Denis-Charles Cisinski has developed a general theory of model structures on presheaf categories...
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In higher category theory in mathematics, a proper model structure is a model structure in which additionally weak equivalences are preserved under pullback...
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Definition A.3.3.1. Cisinski 2019, 2.3.10. Cisinki 2019, Proposition 2.3.13. Lurie 2009, Proposition A.2.8.7. model structure on functors at the nLab...
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2.8. Cisinski 2023, Corollary 4.3.13. Cisinski 2023, Proposition 6.1.2. Cisinski 2023, Corollary 4.1.9. Cisinski 2023, Definition 4.3.1. Cisinski 2023...
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Reedy category (section Reedy model structure)
category". mathoverflow. Barwick, Clark (2007), On Reedy Model Categories, arXiv:0708.2832 Cisinski, Denis-Charles (2023). Higher Categories and Homotopical...
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surjective.[clarification needed] Cisinski 2023, Theorem 3.6.8. Cisinski 2023, Corollary 3.6.6. Cisinski 2023, Theorem 3.9.7. Cisinski, Denis-Charles (2023). Higher...
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1. Cisinski 2023, Definition 5.2.3. Cisinski 2023, Theorem 5.2.10. Cisinski 2023, Corollary 5.3.21. Cisinski 2023, § 5.6.1. and § 5.8.1. Cisinski 2023...
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Definition1.5.1. Cisinski 2019, Theorem 3.6.1. and Theorem 3.1.8. Cisinski 2019, 3.1.30. Cisinski 2019, Example 1.2.7. and Remark 7.8.11. Cisinski 2019, 1.4...
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Bisimplicial set (section Model structures)
Cisinski 2019, 5.5.1. Cisinski 2019, 5.5.1. Cisinski 2019, 5.5.2. Cisinski 2019, Definition 5.5.10. Cisinski 2019, Lemma 5.5.17. Cisinski 2019, Corollary 5...
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(help) Cisinski 2023, Example 2.1.11. Second method Riehl 2014, § 12.2. and § 12.5. harvnb error: no target: CITEREFRiehl2014 (help) Mark Hovey, Model categories...
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1908 – Joseph Leycester Lyne, English monk (born 1837) 1909 – Jakub Bart-Ćišinski, German poet and playwright (born 1856) 1913 – Ralph Rose, American shot...
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Bertrand. "Kan's Ex∞ functor" (PDF). Cisinski 2019, p. 81 Guillou, Definition 6 Guillou, Proposition 1 Cisinski 2019, Equation (3.1.22.4) Guillou, Definition...
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Cisinksi 2019, 4.2.1. Lurie 2009, after Corollary 4.2.1.4. Cisinski 2019, 4.2.1. Cisinski 2019, Proposition 4.2.2. Lurie 2009, Proposition 4.2.1.2. Cisinksi...
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301, MR 2200690 Denis-Charles Cisinski (2006), "Les préfaisceaux comme modèles des types d'homotopie" [Presheaves as models for homotopy types] (PDF), Astérisque...
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& Tierney 2008, Theorem 3.3.5. Quillen 1967, Chapter II. Introduction. Cisinski, Denis-Charles (2023). Higher Categories and Homotopical Algebra (PDF)...
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standard model category structure on simplicial sets and are therefore of fundamental importance. Kan complexes are the fibrant objects in this model category...
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Cisinski 2019, 3.4.14. Lurie 2009, 1.2.9 Overcategories and Undercategories Joyal 2008, Proposition 3.13. Cisinski 2019, Proposition 3.4.17. Cisinski...
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1999, S. 183 Cisinski 2019, 3.8.6. Cisinski 2019, Proposition 3.1.19. Cisinski 2019, Proposition 3.1.18. Cisinski 2019, Lemma 3.1.25. Cisinski 2019, Lemma...
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Glossary of category theory (redirect from Glossary of model categories)
language of category theory in the setting of ∞-categories. Denis-Charles Cisinski, An ∞-category is obtained from a category by replacing the class/set of...
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doi:10.2307/1970841. JSTOR 1970841 – via Math - Côte d'Azur University. Cisinski, Denis-Charles (March 2015). "Higher Categories And Topos Theory(in french)"...
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constant as well. These latter model category structures are constructed using M. Olschok's PhD which generalizes Cisinski's work on the homotopy theory...
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("related mathematics") is taken as: Categories of abstract algebraic structures including representation theory and universal algebra; Homological algebra;...
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