Incidence Coalgebras: Automorphisms and Derivations

We describe automorphisms and derivations of the incidence coalgebra $\text{Co}(X,F)$ of the partially ordered set $X$ over a field $F$. In this case, the fact is significantly used that the dual algebra of the coalgebra $\text{Co}(X,F)$ is isomorphic to the incidence algebra $I(X,F)$ of the partially ordered set $X$ over the field $F$.