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All diagrams commute.
The actual theorem is Mac Lane's Coherence TheoremMac Lane's Coherence Theorem or any of a number of other coherence theoremscoherence theorems that guarantee that all category diagrams built from certain elements commute.
The actual theorem is Mac Lane's Coherence Theorem or any of a number of other coherence theorems that guarantee that all category diagrams built from certain elements commute.