Operads of natural operations I: Lattice paths, braces and Hochschild cochains

In this first paper of a series we study various operads of natural operations on Hochschild cochains and relationships between them.

💡 Research Summary

This paper initiates a systematic study of operads that encode all natural operations on Hochschild cochains of an associative algebra A. The authors begin by formalising what “natural” means in this context: an operation is natural if it commutes with every algebra homomorphism, i.e. it is defined purely in terms of the underlying associative structure and not on any particular presentation of A. Such operations are multilinear maps
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