Historical persons in VMs

[Aga Tentakulus]

The question should be, why should Fieschi (Pope Innocent IV) be mentioned in the VM 200 years later? Died 1252.
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Why does the family coat of arms not match. (inclination)
Why does the hat not match.
Why does he have breasts and why is he in a barrel?
Why do you see the white ram in the VM as so important?
I don't see any obvious correspondence.