A complete classification of endomorphisms of Kiselman's semigroup
Luka Andrensek

TL;DR
This paper provides a complete classification of all endomorphisms of Kiselman's semigroup $K_n$, including an isomorphic Boolean matrix monoid, advancing understanding of its algebraic structure.
Contribution
The paper offers the first full classification of endomorphisms of $K_n$ and constructs an isomorphic Boolean matrix monoid, filling a key gap in the algebraic theory of $K_n$.
Findings
Complete classification of endomorphisms of $K_n$
Construction of an isomorphic Boolean matrix monoid
Resolution of the classification question posed by Kudryavtseva and Mazorchuk
Abstract
Kiselman's semigroup was studied by Kudryavtseva and Mazorchuk, who posed the question of whether it is possible to classify all endomorphisms of . In this paper, we provide a complete classification of endomorphisms of and present a Boolean matrix monoid that is isomorphic to .
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