Endomorphism operads of functors
Abstract
We consider the endomorphism operad of a functor, which is roughly the object of natural transformations from (monoidal) powers of that functor to itself. There are many examples from geometry, topology, and algebra where this object has already been implicitly studied. We ask whether the endomorphism operad of the forgetful functor from algebras over an operad to the ground category recovers that operad. The answer is positive for operads in vector spaces over an infinite field, but negative both in vector spaces over finite fields and in sets. Several examples are computed.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.09006
 arXiv:
 arXiv:1906.09006
 Bibcode:
 2019arXiv190609006D
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Topology