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Mateo Carmona (Sep 14 2022 at 00:27):Hi all,
I would like to know who was the first to introduce the "opposite category" notion.
I would say it was in Grothendieck's Tohoku paper. Maybe you know a counterexample of this.
I know that in 40s Mac Lane studied some general duality properties of groups (for example direct and free products). The idea of "reversing the arrows" was already on this time. But in a simple search, I could not find the definition of "opposite category" in Mac Lane or Eilenberg.
(I am trying to create a clear picture of the influence of Grothendieck at the beginning of the field.)
Nathanael Arkor (Sep 14 2022 at 00:44):It was introduced in the original paper General Theory of Natural Equivalences, on page 259.
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Mateo Carmona (Sep 14 2022 at 00:50):Oh, good! Thank you!
Notification Bot (Sep 14 2022 at 00:51):Mateo Carmona has marked this topic as resolved.
Mateo Carmona (Sep 14 2022 at 00:55):My position was not arbitrary, my supposition was shared by Dieudonné's "A history of algebraic and differential topology". But I suspected that this concept was so fundamental that it seemed strange to be defined that late.