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math.AT2026
Stability of persistent path homology of path complexes
Chris Kapulkin, Kyle Koyanagi
We show stability of persistent path homology of path complexes. As a consequence, we deduce the stability of persistent path homology of hypergraphs and of sequence hypergraphs, a…
math.AT2026
Discrete homotopy hypothesis for n-types
Daniel Carranza, Chris Kapulkin
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse…