# Pyknotic objects, I. Basic notions

## TL;DR

This paper introduces pyknotic objects, a new framework of sheaves on compacta that incorporate topological data, facilitating algebraic and homotopical analysis with applications to local fields.

## Contribution

It develops the foundational theory of pyknotic objects, providing basic definitions and examples to bridge topology with algebra and homotopy theory.

## Key findings

- Pyknotic objects unify sheaf theory with topological data.
- They enable new approaches to derived categories of local fields.
- Basic examples illustrate the utility of pyknotic structures.

## 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.

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Source: https://tomesphere.com/paper/1904.09966