# Khudaverdian H. Non-linear homomorphisms of algebras of functions are induced by thick morphisms (abstract)

In 2014 Th. Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $\displaystyle{ L_{\infty} }$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary smooth maps, but are not maps themselves. Nevertheless, they induce pull-backs on $\displaystyle{ C^{\infty} }$ functions. These pull-backs are in general non-linear maps between the algebras of functions which are so-called "non-linear homomorphisms". By definition, this means that their differentials are algebra homomorphisms in the usual sense. The following conjecture was formulated: an arbitrary non-linear homomorphism of algebras of smooth functions is generated by some thick morphism. We prove here this conjecture in the class of formal functionals.