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The minimal nontrivial endomorphism monoids M= End Con (A,F) of congruence lattices of algebras $(A,F)$ defined on a finite set A are described. They correspond (via the Galois connection End-Con) to the maximal nontrivial congruence lattices Con (A,F) investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices Quord (A,F).
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Jakubı́ková-Studenovská et al. (2023) studied this question.
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