Talk:Equivalence of categories
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Is every equivalence between additive categories automatically an additive functor? AxelBoldt 17:24, 26 Jan 2004 (UTC)
I find this hard to believe. Taking a single object, so a ring, doesn't it say more about the multiplicative monoid of the ring determining it, than is likely to be true?
Charles Matthews 17:33, 26 Jan 2004 (UTC)
Yes, but a ring is a preadditive category in our terminology, and for those the conjecture is clearly false; for additive categories it is however true as our own article additive category claims at the very bottom. AxelBoldt 17:36, 26 Jan 2004 (UTC)
Duality vs. Opposite
The article states:
- If a category is equivalent to the dual of another category then one speaks of a duality of categories.
Isn't it more usual to talk of the opposite of a category, rather than its dual? MacLane's CftWM recognises the usage dual, but uses the terminology of opposite instead. I've only seen the term dual category used in informal contexts in recent work. ---- Charles Stewart 11:17, 31 Aug 2004 (UTC)