Strictification

In mathematics, specifically in category theory, a strictification refers to statements of the form “every weak structure of some sort is equivalent to a stricter one.” Such a result was first proven for monoidal categories by Mac Lane, and it is often possible to derive strictifications from coherence results and vice versa.

Monoidal category Every monoidal category is monoidally equivalent to a strict monoidal category. This is (essentially) the Mac Lane coherence theorem.