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Jan 28 at 22:23 vote accept Tim Campion
Jan 12 at 16:35 comment added Tim Campion Ugh I feel silly for not having thought of the ordinal example but I feel a little better knowing that you didnt immediately think of it either and it's also quite nice to have an example in a fine upstanding category of structures like rings! In the ordinal example, $\kappa$ fails to have the compactness with respect to coproducts property i mentioned in an edit, i haven't thought this through for the ring example.
Jan 12 at 16:24 history answered Maxime Ramzi CC BY-SA 4.0