КГТА семинар, 12. октобар 2023.

• 10. Октобар, 2023
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Наредни састанак Семинара биће одржан у четвртак, 12. октобра 2023, у сали 301ф Математичког института САНУ од 12.15.

Предавач: Pierre-Louis Curien, CNRS researcher, IRIF (CNRS and Université Paris Cité)

Наслов предавања: GENERAL COHERENCE THEOREMS ON CW-COMPLEXES AND POLYHEDRAL COMPLEXES

Апстракт:
We formulate and prove a coherence theorem on regular CW-complexes: 1-cells determine cellular paths, and the theorem states that any two such parallel paths (i.e. with the same end 0-cells) are provably equivalent by repetitive discrete transformations along a 2-cell if and only if each path component of the complex is simply connected. A number of coherence theorems of the literature follow as a corollary ((permuto)associahedra for (symmetric) monoidal categories, etc.). The proof is very different from Mac Lane`s original proof which uses rewriting, even if the vocabulary of rewriting theory was not available then. It substantiates Kapranov`s claim of an «instant one-step proof of MacLane`s theorem». We then give a second strictly less general proof of coherence, applying to polyhedral complexes satisfying a certain condition (which is in particular satisfied by all polytopes), that relies on an orientation given by some generic vector, and that retains most of the features of Mac Lane`s original proof. Finally, we shall present a condition on polytopes of a particular kind, the hypergraph polytopes of Došen and Petrić, that allows to retain all the Ingredients of Mac Lane`s original proof. This is a joint work with Guillaume Laplante-Anfossi.

Напомена: Предавања се могу пратити на даљину преко линка:
https://miteam.mi.sanu.ac.rs/call/XZawgjASPavABY37A/2t2yGBvU01onPAP3aSUKiNFb2Skjk-3w5XJruW-yaZh

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https://miteam.mi.sanu.ac.rs/asset/sd3bebvvcBSNtN78B