2021/12/29 by M. Gavrilovich, Gavrilovich, M., K. Pimenov +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2112.14751
openalex publication_date 2021/12/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We observe that the notion of a trivial Serre fibration, a Serre fibration, and being contractible, for finite CW complexes, can be defined in terms of the Quillen lifting property with respect to a single map M-->/ of finite topological spaces (preorders) of size 5 and 3. In particular, we observe that the double Quillen orthogonal M-->/ lr is precisely the class of trivial Serre fibrations if calculated in a certain category of nice topological spaces. This suggests a question whether there is a finitistic/combinatorial definition of a model structure on the category of topological spaces entirely in terms of the single morphism M-->/ apparently related to the Michael continuous selection theory.