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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Vladimir Sotirov has asked a question at contravariant functor.
I’ve thought about considering categories with covariant and contravariant functors as forming a category enriched over $Cat\times Cat$ with a slightly funny non-symmetric monoidal structure, but that doesn’t allow for transformations that mix variance. Perhaps whoever wrote that page was thinking of a similar monoidal structure on $Cat/I$ (with $I$ the walking iso)?
The underlying 1-category can be obtained as the Grothendieck construction applied to the obvious diagram of shape $\mathbb{B} (\mathbb{Z} / 2 \mathbb{Z})$, but I don’t see how to get the 2-cells in a “natural” way.
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