Higher Algebraic K-Theory

By A. Kuku. 2006

1,151 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66628267fb55ca3821d7153447d46681f7972418

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Central extensions of smooth 2–groups and a finite-dimensional string 2–group (2009, background): “A few years later, Quillen introduced the notion of exact category in his work on algebraic K–theory [48].”
Graded Rings and Graded Grothendieck Groups (2014, methodology): “This can be used to calculate the (lower) graded K-theory of graded division algebras (see Proposition 3.6.1, Remark 3.6.2 and Example 3.10.3).”
Homotopy-theoretic aspects of 2-monads (2006, background): “The definitions of weak equivalence and fibration for 2-functors coming from the model structure on 2-Cat of [12] make perfectly good sense for large 2-categories, and it is only size issues which prevent this from making 2-CAT/K into a model category, and sem into a right Quillen functor.”
Hereditary abelian model categories (2015, background): “A Frobenius category is an exact category in the sense of [54], which has enough projectives and enough injectives, but such that the projective objects coincide with the injective objects.”
Semisimplicial spaces (2017, methodology): “In this section, we prove generalisations of Quillen’s Theorems for topological and nonunital categories.”
Chow-Witt groups and Grothendieck-Witt groups of regular schemes (2009, background): “We first recall a result in K-theory that we will use in this section (see for instance [14, Chapter 5, §1] or [17, Chapter II, Exercise 5.16(d)]).”
The Picard crossed module of a braided tensor category (2012, background): “Analogues of (bi-)modules over algebras are (bi-@)module categories over tensor categories [Quillen 1973; Janelidze and Kelly 2001; Ostrik 2003b].”
La réalisation étale et les opérations de Grothendieck (2014, neutral): “(Pour plus de détails, le lecteur est renvoyé à [17] ou à [52, Chap.”
Gorenstein Homological Aspects of Monomorphism Categories via Morita Rings (2015, background): “The monomorphism category MonA is an extension closed additive subcategory of MorA , and this implies that MonA is an exact category in the sense of Quillen [39].”
Isomorphism Conjecture for homotopy K-theory and groups acting on trees (2004, methodology): “For KR this follows from the compatibility of K-theory with directed colimits [22].”
Some Homological Properties of Skew PBW Extensions (2013, methodology): “(5.2) Next we compute the Quillen’s K-groups for skew quantum polynomials, we will see that this computations generalize the results presented in [2].”
A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “According to [51], an exact category is an additive category A with a distinguished class of sequences”