In algebra we consider two structures to "equivalent" iff they are isomorphic. But apparently in the category of categories, equivalent categories needn't be isomorphic. This goes against my intuition of isomorphism, which I so far thought to be the category theoretic "definition" of equivalent. Why, and what's the right way to think about isomorphisms/equivalences?
2026-04-28 17:47:45.1777398465
Why are equivalent categories not the same as isomorphic categories?
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