Abstract
We review a theorem of A. Roig about Quillen model structures on Grothendieck bifibrations and observe that it contains a gap. We reformulate one of its assumptions in order to validate it. As an application to the new version, we introduce the fibred model structure on the category of small categories enriched in a suitable monoidal model category.
Keywords
Bifibration Weak factorisation system Model category Enriched categoryMathematics Subject Classifications (2000)
18D30 18D20 55U35Preview
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References
- 1.Hirschhorn, P.S.: Model categories and their localizations. In: Mathematical Surveys and Monographs, vol. 99, xvi+457 pp. American Mathematical Society, Providence (2003)Google Scholar
- 2.Hovey, M.: Monoidal model categories, 14 pp. (1998) (available at the author’s homepage)Google Scholar
- 3.Jacobs, B.: Categorical logic and type theory. In: Studies in Logic and the Foundations of Mathematics, vol. 141, xviii+760 pp. North-Holland, Amsterdam (1999)Google Scholar
- 4.Kelly, G.M.: Doctrinal adjunction. Category Seminar (Proc. Sem., Sydney, 1972/1973). Lecture Notes in Math., vol. 420, pp. 257–280. Springer, Berlin (1974)Google Scholar
- 5.Kelly, G.M.: Basic enriched category theory. London Mathematical Society Lecture Note Series, vol. 64, 245 pp. Cambridge University Press, Cambridge (1982)zbMATHGoogle Scholar
- 6.Kelly, G.M., Lack, S.: V-Cat is locally presentable or locally bounded if V is so. Theory Appl. Categ. 8, 555–575 (2001, electronic)MathSciNetzbMATHGoogle Scholar
- 7.Roig, A.: Model category structures in bifibred categories. J. Pure Appl. Algebra 95(2), 203–223 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
- 8.Schwede, S., Shipley, B.E.: Algebras and modules in monoidal model categories. Proc. London Math. Soc. (3) 80(2), 491–511 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
- 9.Schwede, S., Shipley, B.E.: Equivalences of monoidal model categories. Algebraic and Geometric Topology 3, 287–334 (2003, electronic)MathSciNetzbMATHCrossRefGoogle Scholar
- 10.Toën, B.: Derived Hall algebras. Duke Math. J. 135(3), 587–615 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
- 11.Wolff, H.: V-cat and V-graph. J. Pure Appl. Algebra 4, 123–135 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
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