2018/09/28 by Christian Sattler, Sattler, Christian
Biochemistry, Genetics and Molecular Biology · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.1809.11168
openalex publication_date 2018/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the homotopy theory of semisimplicial sets constructively and without reference to point-set topology to obtain a constructive model for ω-groupoids. Most of the development is folklore, but for a few results the author is unaware of previously known constructive proofs. These include the statements that the unit of the free simplicial set adjunction is valued in weak equivalences and that the geometric product and cartesian product of fibrant semisimplicial sets are weakly equivalent. We then extend the development to marked semisimplicial sets in order to obtain a constructive model for (ω, 1)-categories.