### Turning retractions of an algebra into an algebra.

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A structure is called homomorphism-homogeneous if every homomorphism between finitely generated substructures of the structure extends to an endomorphism of the structure (P. J. Cameron and J. Nešetřil, 2006). In this paper we introduce oligomorphic transformation monoids in full analogy to oligomorphic permutation groups and use this notion to propose a solution to a problem, posed by Cameron and Nešetřil in 2006, to characterize endomorphism monoids of homomorphism-homogeneous relational structures...

This paper introduces the notion of a strong retract of an algebra and then focuses on strong retracts of unary algebras. We characterize subuniverses of a unary algebra which are carriers of its strong retracts. This characterization enables us to describe the poset of strong retracts of a unary algebra under inclusion. Since this poset is not necessarily a lattice, we give a necessary and sufficient condition for the poset to be a lattice, as well as the full description of the poset.

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