English

Pyknotic objects, I. Basic notions

Algebraic Geometry 2019-05-01 v2 Algebraic Topology Category Theory

Abstract

Pyknotic objects are (hyper)sheaves on the site of compacta. These provide a convenient way to do algebra and homotopy theory with additional topological information present. This appears, for example, when trying to contemplate the derived category of a local field. In this article, we present the basic theory of pyknotic objects, with a view to describing a simple set of everyday examples.

Keywords

Cite

@article{arxiv.1904.09966,
  title  = {Pyknotic objects, I. Basic notions},
  author = {Clark Barwick and Peter Haine},
  journal= {arXiv preprint arXiv:1904.09966},
  year   = {2019}
}

Comments

Comments very welcome. v2: 39 pages. Clarified connection to Clausen & Scholze's condensed mathematics and corrected a subtle error regarding hypercompleteness

R2 v1 2026-06-23T08:46:33.937Z