Independence of the axioms of Quillen's model structure
Abstract
本文探讨模型结构基本公理的独立性问题. 通过完备余挠对等方法，本文构造了四个范畴 $\mathcal{A}$ 及其上的态射类三元组 $(\CoFib(\mathcal{A}), \ \Fib(\mathcal{A}), \ \Weq(\mathcal{A}))$, 每个三元组满足 Quillen 的模型结构中的三条公理但违反第四条公理. 这些构造表明了 Quillen 模型结构定义中四条公理的独立性, 即, 没有任何一条公理是其余公理的逻辑推论.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Geometric and Algebraic Topology
Publication details
- Journal / source
- Scientia Sinica Mathematica
- Publication date
- 1 March 2026
- Language
- EN