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Sep 20 at 20:02 comment added Student It took me a while to understand this answer, and wow it's good! (1) I wonder, is $U^G: C^{T^G} \to C$ also initial among functors to $C$ that admit left adjoints? (I know what 'monadic' means here, but I don't feel natural to consider the initial object among monadic functors to $C$; partly because I don't understand why we should consider only the monadic ones.) (2) (How) Does your answer fit into Mike Shulman's?
Jan 14 at 19:50 history answered Tom Leinster CC BY-SA 4.0