Pyknotic objects, I. Basic notions
arXiv:1904.09966
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.
Comments very welcome. v2: 39 pages. Clarified connection to Clausen & Scholze's condensed mathematics and corrected a subtle error regarding hypercompleteness