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- Q-construction abstract "In algebra, Quillen's Q-construction associates to an exact category (e.g., an abelian category) an algebraic K-theory. More precisely, given an exact category C, the construction creates a topological space so that is the Grothendieck group of C and, when C is the category of finitely generated projective modules over a ring R, for , is the i-th K-group of R in the classical sense. (The notation "+" is because it actually provides a model for Quillen's +-construction.) One putsand call it the i-th K-group of C. Similarly, the i-th K-group of C with coefficients in a group G is defined as the homotopy group with coefficients:.The construction is widely applicable and is used to define an algebraic K-theory in a non-classical context. For example, one can define equivariant K-theory as of of the category of equivariant sheaves on a scheme.Waldhausen's S-construction generalizes the Q-construction; in fact, the former, which uses a more general Waldhausen category, produces a spectrum instead of a space. Grayson's binary complex also gives a construction of algebraic K-theory for exact categories.Every ring homomorphism induces and thus where is the category of finitely generated projective modules over R. One can easily show this map (called transfer) agrees with one defined in Milnor's Introduction to algebraic K-theory. The construction is also compatible with the suspension of a ring (cf. Grayson).".
- Q-construction wikiPageExternalLink Kbook.html.
- Q-construction wikiPageExternalLink HigherAlgKThyII.pdf.
- Q-construction wikiPageID "41403415".
- Q-construction wikiPageRevisionID "589510971".
- Q-construction subject Category:Algebra.
- Q-construction comment "In algebra, Quillen's Q-construction associates to an exact category (e.g., an abelian category) an algebraic K-theory. More precisely, given an exact category C, the construction creates a topological space so that is the Grothendieck group of C and, when C is the category of finitely generated projective modules over a ring R, for , is the i-th K-group of R in the classical sense.".
- Q-construction label "Q-construction".
- Q-construction sameAs m.0zrrxlm.
- Q-construction sameAs Q17099681.
- Q-construction sameAs Q17099681.
- Q-construction wasDerivedFrom Q-construction?oldid=589510971.
- Q-construction isPrimaryTopicOf Q-construction.