Monoidal categories are everywhere. They can be defined as pseudomonoids in the monoidal bicategory $(\mathsf{Cat},\times)$ of categories, functors and natural transformations. By turning directions of arrows around, one obtains the notion of pseudocomonoid in a monoidal bicategory. Have these be studied before? Call a pseudocomonoid in the monoidal bicategory $(\mathsf{Cat},\times)$ a comonoidal category. Why are monoidal categories so prevalent, but comonoidal ones are not?
2026-02-23 06:33:16.1771828396
Comonoidal categories?
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