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R. Gregorič, Operads and multicategories

Date: 14. 10. 2016
Source: Topology seminar
Ponedeljek, 17. oktober 2016 ob 12.15 uri v predavalnici 3.06 na Jadranski 21
 
Operads and multicategories  
 
The notion of an operad was first introduced by Peter J. May in the sixties to help encode homotopical analogues of commutativity in the study of iterated loop spaces. They have taken on a life of their own and found important applications in various areas of topology, algebra, geometry and even physics. 
In this lecture, we will introduce the definition of an operad and its algebras and look at some basic examples. Then we will start over and observe the seemingly unconnected notion of multicategories, before seeing how operads naturally pop up in that context. This will hopefully shine some light on both why operads are such essential objects and also on their connection to monoidal categories. 
In future seminars we hope to present more explicit applications to topology, namely to prove the recognition principle for iterated loop spaces.