Monoidal categories are a type of category equipped with a tensor product, which allows for the combination of objects and morphisms in a way that respects the category's structure. They include an identity object and a set of natural isomorphisms that express the associative and unital properties of the tensor product. This concept is crucial when exploring functor types, as they can act in structured ways on the objects and morphisms, and play a significant role in understanding adjunctions through their ability to express relationships between different categories.
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