1
$\begingroup$

Given posets $A, B$, we denote by $\text{Hom}(A,B)$ the collection of order-preserving functions $f:A\to B$. We put a partial order $\leq_{\text{Hom}(A,B)}$ on $\text{Hom}(A,B)$ by setting $$f \leq_{\text{Hom}(A,B)} g \iff f(a) \leq g(a) \text{ for all } a\in A.$$

Question. Are there connected posets $P\not \cong Q$ such that $\text{Hom}(P,P) \cong \text{Hom}(Q,Q)$?

Improve this question
$\endgroup$
1
  • $\begingroup$ I think it would be a very nice gesture to inform the reader of what you already know about this problem, to avoid having people waste time. For instance, you are mentioned in a footnote here, arxiv.org/pdf/2005.03255.pdf, which recalls the finite case covered by results of Duffus and Wille. $\endgroup$
    – Todd Trimble
    Commented Apr 25, 2022 at 16:16

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .