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3 votes
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Cartesian monoidal star-autonomous categories

[I'm going to assume $S' \cong S$, which holds in every symmetric monoidal $*$-autonomous category. (See e.g. Lemma 5.6 of this paper.) This applies here since cartesianness implies symmetry. Part of ...
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4 votes
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Star-autonomous categories are categorifications of Boolean algebras?

The starting point for decategorification is the observation that a category in which any parallel arrows are equal must necessarily be a preorder. Restricting to skeletal categories makes it a poset. ...
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3 votes
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Strictification of $\mathcal{V}$-pseudofunctors

In section 4 of my paper Not every pseudoalgebra is equivalent to a strict one, I sketched a proof that for any monoidal 2-category $\mathcal{W}$ with small sums preserved on both sides by its tensor ...
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