English

The localic compact interval is an Escard\'o-Simpson interval object

Category Theory 2018-01-03 v1

Abstract

The locale corresponding to the real interval [-1,1] is an interval object, in the sense of Escard\'o and Simpson, in the category of locales. The map c from 2^\omega to [-1,1], mapping a stream s of signs +1 or -1 to \Sum_{i=1}^\infty s_i 2^{-i}, is a proper localic surjection; it is also expressed as a coequalizer.

Cite

@article{arxiv.1506.07995,
  title  = {The localic compact interval is an Escard\'o-Simpson interval object},
  author = {Steven Vickers},
  journal= {arXiv preprint arXiv:1506.07995},
  year   = {2018}
}

Comments

22 pages

R2 v1 2026-06-22T10:00:43.617Z