CatDat

• notation: $(-)^{\op}: \Mon \to \Mon$
• Source: category of monoids
• Target: category of monoids
• Left adjoint functor: $(-)^{\op}$
• Right adjoint functor: $(-)^{\op}$
• Related functors: $(-)^{\op}$
• nLab Link

This functor maps a monoid $M$ to its opposite monoid $M^{\op}$ which has the multiplication $a *^{\op} b \coloneqq a * b$. A monoid homomorphism $f : M \to N$ is also a monoid homomorphism $f^{\op} : M^{\op} \to N^{\op}$.