We introduce a functorial construction which, from a monoid, produces a
set-operad. We obtain new (symmetric or not) operads as suboperads or quotients
of the operads obtained from usual monoids such as the additive and
multiplicative monoids of integers and cyclic monoids. They involve various
familiar combinatorial objects: endofunctions, parking functions, packed words,
permutations, planar rooted trees, trees with a fixed arity, Schr\"oder trees,
Motzkin words, integer compositions, directed animals, and segmented integer
compositions. We also recover some already known (symmetric or not) operads:
the magmatic operad, the associative commutative operad, the diassociative
operad, and the triassociative operad. We provide presentations by generators
and relations of all constructed nonsymmetric operads.Comment: 42 pages. Complete version of the extended abstracts arXiv:1208.0920
and arXiv:1208.092
