Cyclic Cohomology of Coalgebras, Coderivations and De Rham Cohomology

We define and study cyclic cohomology of a coalgebra. Explicit computations are done for the tensor coalgebra of a vector space and for the topological coalgebra of distributions over a compact smooth manifold. The Monta‐Takeuchi invanance of cyclic cohomology and an exciston Theorem are proved.