English

Generalized point-free spaces, pointwise

Category Theory 2022-06-03 v1

Abstract

We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results using generalized points support a fully pointwise notation for these essentially point-free structures. This includes some from dependent type theory to deal with bundles as continuous space-valued maps, mapping base point to fibre.

Keywords

Cite

@article{arxiv.2206.01113,
  title  = {Generalized point-free spaces, pointwise},
  author = {Steven Vickers},
  journal= {arXiv preprint arXiv:2206.01113},
  year   = {2022}
}

Comments

32 pages

R2 v1 2026-06-24T11:37:21.442Z