Implication Details
Claim: If a category is an elementary topos and is locally essentially small, then it is well-copowered.
Proof: This follows from Mac Lane & Moerdijk, Theorem IV.7.8 (and Prop. I.3.1).
Claim: If a category is an elementary topos and is locally essentially small, then it is well-copowered.
Proof: This follows from Mac Lane & Moerdijk, Theorem IV.7.8 (and Prop. I.3.1).