有效Kan纤维化的实例与余纤生成
Examples and cofibrant generation of effective Kan fibrations
AI总结：
该研究针对单纯同伦理论中的有效Kan纤维化，证明单纯Malcev代数是有效Kan复形且其为代数弱因子分解系统右类，还提出两种强化形式并验证结果适用。
摘要：
我们对有效Kan纤维化理论做出两项贡献，有效Kan纤维化是单纯同伦理论中起核心作用的Kan纤维化概念的更显式版本。我们证明单纯Malcev代数是有效Kan复形，且有效Kan纤维化可被视为代数弱因子分解系统中的右类。此外，我们引入有效Kan纤维化概念的两种强化形式：对称有效Kan纤维化与偏好退化Kan纤维化，并证明前述结果对这些强化形式同样成立。
英文摘要：
We will show make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that simplicial Malcev algebras are effective Kan complexes and that the effective Kan fibrations can be seen as the right class in an algebraic weak factorisation system. In addition, we will introduce two strengthenings of the notion of an effective Kan fibration, the symmetric effective and degenerate-preferring Kan fibrations, and show that the previous results holds for these strengthenings as well.
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