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Jeudi 4 Novembre
| Heure: |
10:00 - 12:00 |
| Lieu: |
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 |
| Résumé: |
Topologie algébrique - Infinity-operads as analytic monads - |
| Description: |
Rune HaugsengJoyal proved that symmetric sequences in sets (or "species") can be
identified with certain endofunctors of Set, namely the "analytic"
functors. Under this identification the composition product on symmetric
sequences corresponds to composition of endofunctors,
and this allows us to identify operads in Set with certain "analytic"
monads. Moreover, the monad corresponding to an operad O is precisely
the monad for free O-algebras in Set. In this talk I will explain how to
obtain an analogous identification for infinity-operads:
assigning to an infinity-operad O (in Lurie's sense) the monad for free
O-algebras in spaces identifies infinity-operads with analytic monads.
This builds on previous work with Gepner and Kock where we developed the
theory of analytic monads in the infinity-categorical
setting. |
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