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

Pyknotic objects, I. Basic notions