Abstract
In this paper we study the simplicial structure of the complex \(C^{\bullet}((A,B,\varepsilon); M)\), associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object \(\mathcal{B}(A,B,\varepsilon)\), which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cyclic (co)homology and establish some of its properties (Theorems 3.9 and 4.11).