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Answer by S.C. for Which direction does a lax dinatural transformation go?

This is a very loose answer since it's based on something that, as far as I know, has not been fully formalized. The key idea is that of what I might call a "dependent arrow" between two objects.The...

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Which direction does a lax dinatural transformation go?

In 2-category theory we often encounter notions with noninvertible coherence 2-cells, in which case there is a choice about which way the 2-cell should point. Generally, one of these directions is...

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