Regular polygraphs and a homotopical pasting theorem
Clémence Chenavat
Tallinn University of Technology
https://chanavat.site/
Date(s) : 08/10/2026 iCal
11h00 - 12h30
A directed complex is a combinatorial object that encodes the data necessary to define a regular polygraph. I will start by presenting Hadzihasanovic's theory of higher-categorical diagrams, whose basic objects (the atoms and molecules) are the shapes with which directed complexes are built. I will then explain how to generate a strict w-category from a directed complex, and why this construction does not always produce a polygraph unless we impose on strict w-categories higher exchange laws prescribed by combinatorial topology. Finally, I will present a homotopical pasting theorem, extending recent results of Campion, establishing that a certain class of directed complexes produces homotopy polygraphs, meaning that the cellular extensions defining them are homotopy pushouts in the theory of (oo, n)-categories.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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