A topos is a category modeled after the properties of the category of sets. More precisely, a category 
is a topos if 
has finite limits and every object
of 
has a power
object (Barr and Wells 1985, p. 75).
The subterminal objects of a topos 
form the Heyting algebra 
, where 
is a terminal object. Its
elements interpret propositions in the internal intuitionistic logic of 
(Mac Lane and Moerdijk 1994).
Ye and Xu (2026) claim that the free Heyting algebra 
on two generators cannot occur as
for any topos 
. Consequently, not every Heyting
algebra can be realized as the lattice of subterminal
objects of a topos. The claim has not received independent review.
