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Jan 12, 2011 at 17:04 comment added Ben Wieland The first example of a rigidification theorem like this is that a monoidal category is equivalent to a strict monoidal category. One adds new objects with names like $A\Box B\Box C$, with morphisms by making them isomorphic to $(A\Box B)\Box C$. Another way to say this is that one forms the free strict monoidal category, but then changes the morphisms to make it equivalent to the old category.
Jan 12, 2011 at 5:23 comment added Mariano Suárez-Álvarez What do you mean by all the shoulds in the first paragraph?
Jan 12, 2011 at 5:14 history answered Ben Wieland CC BY-SA 2.5