Opposite Category

up:: 028 MOC Category Theory

Given a Category $C$, its opposite category $C^{op}$ is defined as $C$ but with all morphisms flipped. That is,

• $Ob(C^{op})=Ob(C)$
• $\forall x,y\in Ob(C^{op}):Ho{m}_{C^{op}}(x,y)=Ho{m}_C(y,x)$

Properties

• Any theorem proved for a category $C$ will also be valid for its opposite category $C^{op}$

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References