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A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a(pre-)Lie algebra homomorphism between them. We give chomologies ofpre-Lie-morphism triples. As an application, we study the infinitesimaldeformations of pre-Lie-morphism triples. Finally, we show that the cohomologyof the pre-Lie-morphism triple can be deduced from a new cohomology of theLie-morphism triple.

Cohomologies and deformations of pre-Lie-morphism triples