3 papers
math.DS2026
From Nilspace Theory to Simplicial Homotopy Theory
Noa Bihlmaier, Nick Ruoff
We construct a faithful functor from the category of cubespaces, arising in structured ergodic theory and nilspace theory, to the category of (condensed) simplicial sets. This func…
math.DS2026
A Categorical Approach to Nilspace Theory
Noa Bihlmaier, Nick Ruoff
Originating in ergodic structure theory, nilspace theory is concerned with the study of cubical spaces. A first key result in this theory, the weak structure theorem, is the repres…
math.CT2025
Aspects of Condensed Mathematics -- From Abstract Nonsense to Ergodic Theory
Noa Bihlmaier, Nick Ruoff, Philipp Schmale
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sec…