Implication Details
Claim: If a category is essentially finite and has pullbacks, then it has wide pullbacks.
Proof: Each slice category has finite products and is essentially finite, hence has all products by this result followed by this result.
Claim: If a category is essentially finite and has pullbacks, then it has wide pullbacks.
Proof: Each slice category has finite products and is essentially finite, hence has all products by this result followed by this result.