The effective model structure and -groupoid objects
The effective model structure and -groupoid objects
复制标题
有效的模型结构和-groupoid对象
DOI：
10.1017/fms.2022.13
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Gambino N
中科院分区：
文献类型：
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作者：
Gambino N
对于一类有限的限制和行为良好的可数余产品，我们构建了一个模型结构，称为有效的模型结构，在类的单纯对象，推广的Kan-Quillen模型结构的单纯集。然后，我们证明了有效的模型结构是左和右适当的，并满足下降的意义下的Rezk。由此，我们得到了伴随-范畴有有限极限，余极限满足下降，当是但不是一般的高拓扑时，是局部笛卡尔闭的。我们还提出了一个有效的模型结构的范畴，表明它是完整的子类别的预层上跨越的Kan复杂的，结果表明一个密切的类比与理论的精确完成。
For a category with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in , generalising the Kan–Quillen model structure on simplicial sets. We then prove that the effective model structure is left and right proper and satisfies descent in the sense of Rezk. As a consequence, we obtain that the associated -category has finite limits, colimits satisfying descent, and is locally Cartesian closed when is but is not a higher topos in general. We also characterise the -category presented by the effective model structure, showing that it is the full sub-category of presheaves on spanned by Kan complexes in , a result that suggests a close analogy with the theory of exact completions.