Moment categories and operads

Clemens Berger – 30 April 2014, 7 May 2014

Moment categories are equipped with a system of split idempotent endomorphisms, called moments, such that each morphism is fixed by a well-determined target moment.

Each moment category of finite type defines a specific type of operad which records the combinatorics of partitioning moments into elementary ones. In this way the notions of symmetric, non-symmetric and n-operad correspond to moment structures on Gamma (Segal), Delta (Eilenberg) and Theta_n (Joyal) respectively.