Finn Lawler
allegory (Rev #3)
Recall the notion of a unitary pre-tabular allegory. Bicategories of relations are equivalent, but this has yet to be shown rigorously and published, as far as I’m aware. This PDF file makes precise the argument at bicategory of relations.
Let be a unitary pre-tabular allegory.
Lemma
If and are maps, then
Proof
Let . Then and , by the modular law and the fact that projections tabulate top elements. So if and only if it is a map.
For the unit inequality, we have
The second equality follows from distributivity , which is an equality because .
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