Endomorphism operad

Example 12.1.9 (Endomorphism operad). For an object \(A\) of a symmetric monoidal category \(C\), we may form the endomorphism operad \(\oEnd _C(A)\), given by \(\oEnd _C(A)(n) := \Hom _C(A^{\otimes n}, A)\). Composition is induced by composition in \(C\) and the associativity isomorphisms for tensor products. The right action of \(\Sigma _n\) is given by precomposition with the symmetry isomorphisms of \(A^{\otimes n}\), using the convention from the display above.