MATH.18:11 - SoTA-Echoing

Fong and Spivak’s Seven Sketches in Compositionality, §§1.2-1.3, develops order, joins and what their maps preserve. The adopted contribution is to compare an observation or transformation by the operations it carries, including the ones it loses. The order-and-operation construction here makes that question usable when the accounts start from different primitives.

Riehl’s Category Theory in Context, §1.5, supplies equivalence through functors and compatible isomorphisms. It supports the family-level comparison. A claim about translated theorems additionally depends on the chosen logic and interpretation.

For a prepared change of coordinates, explicit inverse maps can be enough. A broader account comparison becomes useful when available operations, assumptions or quantifiers differ. The present method combines these alternatives according to the consequence to be transferred.