# mathlibdocumentation

category_theory.monoidal.skeleton

# The monoid on the skeleton of a monoidal category #

The skeleton of a monoidal category is a monoid.

If C is monoidal and skeletal, it is a monoid.

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If C is braided and skeletal, it is a commutative monoid.

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The skeleton of a monoidal category has a monoidal structure itself, induced by the equivalence.

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@[instance]

The skeleton of a monoidal category can be viewed as a monoid, where the multiplication is given by the tensor product, and satisfies the monoid axioms since it is a skeleton.

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