2003/01/09 by John L. Bell, Bell, John L. · 1 citation
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0301034
34 pages
arxiv created 2003/01/11 · arxiv updated 2009/11/30
The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the present paper the covering concept - here called a cover scheme -is presented and developed in the simple case when the underlying category is a preordered set. The relationship between cover schemes, frames (complete Heyting algebras), Kripke models, and frame-valued set theory is discussed. Finally cover schemes and frame-valued set theory are applied in the context of Markopoulou's 1999 account of discrete spacetime as sets "evolving" over a causal set.