题目: Introduction to operadic categories

报告人：Michael Batanin (National Research University Higher School of Economics , Moscow, Russia)

时间及地点：10月8日（周四）16:00-17:30 东区第五教学楼5201

                     10月9日（周五）16:00-17:30 东区第五教学楼5204

摘要:

Operadic categories is a tool designed to organize within a common framework many multivariable algebraic structures. This tool was introduced by Batanin and Markl in 2015.Very briefly, an operadic category is a category O over the category of finite sets Fin  whose morphisms are equipped with an abstract  fiber functor. The category Fin is the most basic example of an operadic category (in fact this is the terminal operadic category)  whose fiber functor is given by a pullback that is just a  a preimage of  a point. But in many interesting cases  the fiber is not given by a pullback.  

Every operadic category O has an associated category of O-operads (and O-cooperads) and each operad has a category of algebras. Examples include classical May's operads (which are Fin-operads in this classification), PROPs, properads, cyclic and modular operads, Batanin's n-operads and many more well known and  new structures.   

In my lectures I will touch only a basic theory of operadic categories with emphasis on examples in the first lecture. Then I will show that operadic categories admit their own interesting Category Theory and how classical coloured symmetric operads (in Set) is just a full subcategory of the category of operatic categories.