Abstract
$ P $-Ehresmann semigroups introduced by Jones are natural generalizations of Ehresmann semigroups. The aim of this paper is to introduce and describe projection-primitive $ P $-Ehresmann semigroups. More specifically, it is proved that a projection-primitive $ P $-Ehresmann semigroup is either isomorphic to a Rees matrix semigroup over a monoid with some natural conditions or a generalized category with zero adjoined.
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