opposite monoid functor

 algebra
Notation (−)op:Mon→Mon(-)^{\op}: \Mon \to \Mon Domain category of monoidsCodomain category of monoidsLeft adjoint opposite monoid functorRight adjoint opposite monoid functor Related (−)op(-)^{\op} External nLab Link

This functor maps a monoid MM to its opposite monoid MopM^{\op} which has the multiplication a∗opb≔a∗ba *^{\op} b \coloneqq a * b. A monoid homomorphism f:M→Nf : M \to N is also a monoid homomorphism fop:Mop→Nopf^{\op} : M^{\op} \to N^{\op}.

Satisfied Properties

Assigned properties

Deduced properties

Unsatisfied Properties

Assigned properties

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Deduced properties*

*This also uses the deduced satisfied properties.

Unknown properties

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Indistinguishable functors

These functors in the database currently have exactly the same properties as the opposite monoid functor. This indicates that the data may be incomplete or that a distinguishing property may be missing from the database.