2018/08/02 by Andrew Swan, Swan, Andrew
Computer Science · Mathematics · #03F55 #55U35 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1808.00915
openalex publication_date 2018/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a general technique for constructing a functorial choice of very good paths objects, which can be used to implement identity types in models of type theories in direct manner with little reliance on general coherence results. We give a simple proof that applies in algebraic model structures that possess a notion of structured weak equivalence, in a sense that we define here. We then give a more direct proof that applies both to the original BCH cubical set model and more recent variants. We give an explanation how this construction relates to the one used in the CCHM cubical set model of type theory.