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