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Asad Saeeduddin (Jul 07 2020 at 04:22):Is it possible to generalize the concept of a tensorial strength for an endofunctor (which pertains to Cat) so that it can be stated for any 2-category? There is a paper called "Arrows are Strong Monads" that does something like this for the 2-category Prof, but I'm having a really hard time reconciling the equipment resulting from their definition of strength in Prof with what we have for a strength in Cat. I think it would clarify things a lot if someone knows of a way to formally state the definition of tensorial strength in terms of the equipment of a 2-category (plus whatever else is necessary).
John Baez (Jul 07 2020 at 05:33):The nLab approaches to "tensorial strength" seem so elegant and abstract that it should be possible to generalize them from Cat to another 2-category with suitable structure (monoidal for starters).