activity
20192025
most citedThe Szymczak Functor on the Category of Finite Sets and Finite Relations

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

math.DS2025

Linear Relations of Finite Length Modules are Shift Equivalent to Maps

Bartosz Furmanek, Filip Oskar Łanecki, Mateusz Przybylski +1

Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled…

math.DS2024

A Complete Invariant for Shift Equivalence for Boolean Matrices and Finite Relations

Ethan Akin, Marian Mrozek, Mateusz Przybylski +1

We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components,…

math.DS2022★ 1 cited

The Szymczak Functor on the Category of Finite Sets and Finite Relations

Mateusz Przybylski, Marian Mrozek, Jim Wiseman

The Szymczak functor is a tool used to construct the Conley index for dynamical systems with discrete time. We present an algorithmizable classification of isomorphism classes in t…

math.AT2021

Morse theory for loop-free categories

Michał Lipiński, David Mosquera-Lois, Mateusz Przybylski

We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and in…

math.DS2019

Conley index approach to sampled dynamics

Bogdan Batko, Konstantin Mischaikow, Marian Mrozek +1

The topological method for the reconstruction of dynamics from time series [K. Mischaikow, M. Mrozek, J. Reiss, A. Szymczak. Construction of Symbolic Dynamics from Experimental Tim…