In mathematics, a Q-category or almost quotient category[1] is a category that is a "milder version of a Grothendieck site."[2] A Q-category is a coreflective subcategory.[1][clarification needed] The Q stands for a quotient.

The concept of Q-categories was introduced by Alexander Rosenberg in 1988.[2] The motivation for the notion was its use in noncommutative algebraic geometry; in this formalism, noncommutative spaces are defined as sheaves on Q-categories.

Definition

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A Q-category is defined by the formula[1][further explanation needed]  where   is the left adjoint in a pair of adjoint functors and is a full and faithful functor.

Examples

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References

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  1. ^ a b c d e f Škoda, Zoran; Schreiber, Urs; Mrđen, Rafael; Fritz, Tobias (14 September 2017). "Q-category". nLab. Retrieved 25 March 2023.
  2. ^ a b Kontsevich & Rosenberg 2004a, § 1.
  • Kontsevich, Maxim; Rosenberg, Alexander (2004a). "Noncommutative spaces" (PDF). ncatlab.org. Retrieved 25 March 2023.
  • Alexander Rosenberg, Q-categories, sheaves and localization, (in Russian) Seminar on supermanifolds 25, Leites ed. Stockholms Universitet 1988.

Further reading

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