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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 21st 2016
   • (edited Feb 21st 2016)
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexFor various reasons, I've begun looking at the category of Moore closure operators. By this I mean the category whose objects are pairs $(X, c)$ where $c: P X \to P X$ is a [[Moore closure]] operator, and a morphism $(X, c) \to (Y, d)$ is a function $f: X \to Y$ such that the inverse image $f^\ast: P Y \to P X$ is a morphism of monads (so $c \circ f^\ast \leq f^\ast \circ d$). Does anyone know if this has been studied, and where?

   For various reasons, I’ve begun looking at the category of Moore closure operators. By this I mean the category whose objects are pairs $(X, c)$ where $c: P X \to P X$ is a Moore closure operator, and a morphism $(X, c) \to (Y, d)$ is a function $f: X \to Y$ such that the inverse image $f^\ast: P Y \to P X$ is a morphism of monads (so $c \circ f^\ast \leq f^\ast \circ d$).

   Does anyone know if this has been studied, and where?