English

Shape theory for condensed anima

Algebraic Topology 2026-05-11 v1 Category Theory

Abstract

We give different perspectives on the notion of shape for condensed anima. We prove that it recovers more classical notions of shape for topological spaces in the cases of all paracompact compactly generated spaces and all locally contractible spaces. These recovering statements imply and extend comparison results on sheaf and condensed cohomology by Clausen-Scholze and Haine. Another homotopy-theoretical direction for condensed anima are their condensed homotopy groups. Connected to this, we give a description of the underlying topological group functor on condensed groups via quasi-topological groups.

Keywords

Cite

@article{arxiv.2605.07843,
  title  = {Shape theory for condensed anima},
  author = {Catrin Mair},
  journal= {arXiv preprint arXiv:2605.07843},
  year   = {2026}
}

Comments

34 pages, partially expands results from arXiv:2105.07888, comments are welcome!

R2 v1 2026-07-01T12:57:56.652Z