2019/12/13 by Jonas Frey, Frey, Jonas · 2 citations
Mathematics · #03G30 #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.1912.06726
openalex publication_date 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a category of fibrant objects ℂ⟨ P⟩ in the sense of K. Brown from any indexed frame (a kind of indexed poset generalizing triposes) P, and show that its homotopy category is the Barr-exact category ℂ[P] of partial equivalence relations and compatible functional relations. In particular this gives a presentation of realizability toposes as homotopy categories. We give criteria for the existence of left and right derived functors to functors ℂ⟨Φ⟩ : ℂ⟨ P⟩→ ℂ⟨ Q⟩ induced by finite-meet-preserving transformations Φ : P → Q between indexed frames.