Overcategories and undercategories of cofibrantly generated model categories

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2021-10-13 DOI:10.1007/s40062-021-00294-4

Philip S. Hirschhorn

引用次数: 6

Abstract

Let \(\mathcal {M}\) be a model category and let Z be an object of \(\mathcal {M}\). We show that if \(\mathcal {M}\) is cofibrantly generated, cellular, left proper, or right proper, then both the model category of objects of \(\mathcal {M}\) over Z and the model category of objects of \(\mathcal {M}\) under Z are as well.

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共同生成的模型类别的超类别和下类别

设\(\mathcal {M}\)为模型范畴，设Z为\(\mathcal {M}\)的对象。我们证明，如果\(\mathcal {M}\)是共纤维生成的、元胞的、左固有的或右固有的，那么\(\mathcal {M}\)在Z上的对象的模型类别和\(\mathcal {M}\)在Z下的对象的模型类别也是如此。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.