On Completions of Posets with Operators
Xia Zhang, Jan Paseka and Wen Ma
In this note, we study completions of posets with a closure operation. Firstly, we show that every such completion is injective in the category of posets with a closure operation with respect to a subclass of order embeddings. Moreover, we show how to construct injective hulls for arbitrary posets with a closure operation.
Keywords: poset with an operator, order-embedding, lax morphism, completion, sup-algebra, injective object, injective hull