additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
The Quillen Q-construction (Quillen 72) is a tool for producing the algebraic K-theory of a Quillen exact category $\mathcal{C}$. The Quillen Q-construction is generalized (Waldhausen 83, section 1.9) by the Waldhausen S-construction which applies more generally to Waldhausen categories. (However, the Quillen Dévissage theorem? does not generalize to Waldhausen categories.)
Both these constructions appear in stable homotopy theory as special cases of the concept of algebraic K-theory of a stable (∞,1)-category (Haugseng 10, Barwick 13).
The construction is due to
Notes in Math., Vol. 341
The generalization to the Waldhausen S-construction is due to
Refinement of the construction to stable (∞,1)-categories and exact (infinity,1)-categories? is discussed in
Rune Haugseng, the Q-construction for stable $\infty$-Categories, 2010 (pdf)
Clark Barwick, On the Q construction for exact quasicategories (arXiv:1301.4725)
C. Barwick, On exact infinity-categories and the Theorem of the Heart, arXiv:1212.5232.
See also
Last revised on September 16, 2015 at 06:20:15. See the history of this page for a list of all contributions to it.