3 ms·

If two categories are related by a functor, does that imply that the first category is isomorphic to the second category? (I'm very new to this topic, but I ha

• j2kun 12y ago
  That's half of it. If you have another functor going the other way, with some properties on how the two functors relate, then you get what's called an equivalence of categories. [1] Basically, you need both ways to compose the two functors to be "equivalent" to the identity functor in each category (equivalent as shown by a reversible natural transformation). [1]: http://en.wikipedia.org/wiki/Equivalence_of_categories http://en.wikipedia.org/wiki/Equivalence_of_categories