[[!redirects opposite (0,1)-precategory]] #Contents# * table of contents {:toc} ## Definition ## Given a [[preorder]] or (0,1)-precategory $P \coloneqq (F(P), \leq)$, an __opposite preorder__ or __opposite (0,1)-precategory__ is a preorder $P^\op \coloneqq (F(P), \geq)$ with $\geq$ defined as $$a:F(P), b:F(P) \vdash a \geq b \coloneqq b \leq a $$ where $F$ is the forgetful functor that gets the underlying type for a preorder. ## See also ## * [[preorder]]