Results 1 to 10 of about 3,101 (70)

From triangulated categories to module categories via localization II: calculus of fractions [PDF]

Journal of the London Mathematical Society, 2012
We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions.
Buan, Aslak Bakke, Marsh, Bethany
openaire   +3 more sources

Blanchfield and Seifert algebra in high-dimensional boundary link theory I: Algebraic K-theory [PDF]

, 2005
The classification of high-dimensional mu-component boundary links motivates decomposition theorems for the algebraic K-groups of the group ring A[F_mu] and the noncommutative Cohn localization Sigma^{-1}A[F_mu], for any mu>0 and an arbitrary ring A ...
Andrew Ranicki, Ara, Bass, Bass, Berrick, Borceux, Cappell, Cappell, Desmond Sheiham, Duval, Farber, Farber, Farber, Gabriel, Gabriel, Gersten, Gillet, Grayson, Gutiérrez, Haghany, Keller, Levine, Levine, Liang, Milnor, Quillen, Ranicki, Ranicki, Ranicki, Sato, Schlichting, Schofield, Sheiham, Sheiham, Smythe, Stallings, Thomason, Trotter, Waldhausen, Waldhausen, Waldhausen, Waldhausen   +41 more
core   +7 more sources

From fractions to complete Segal spaces [PDF]

, 2015
We show that the Rezk classification diagram of a relative category admitting a homotopical version of the two-sided calculus of fractions is a Segal space up to Reedy-fibrant replacement.
Low, Zhen Lin, Mazel-Gee, Aaron
core   +1 more source

Coherent Presentations of Monoidal Categories [PDF]

, 2017
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms.
Curien, Pierre-Louis, Mimram, Samuel
core   +4 more sources

Principal infinity-bundles - Presentations [PDF]

, 2012
We discuss two aspects of the presentation of the theory of principal infinity-bundles in an infinity-topos, introduced in [NSSa], in terms of categories of simplicial (pre)sheaves.
Nikolaus, Thomas, Schreiber, Urs, Stevenson, Danny   +2 more
core   +3 more sources

Quotient triangulated categories [PDF]

, 2006
For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b({\rm add} T)$ and the stable category of the Frobenius category of $T$-Cohen-Macaulay modules is investigated.
Chen, Xiao-Wu, Zhang, Pu
core   +3 more sources

Grothendieck categories as a bilocalization of linear sites

, 2017
We prove that the 2-category Grt of Grothendieck abelian categories with colimit preserving functors and natural transformations is a bicategory of fractions in the sense of Pronk of the 2-category Site of linear sites with continuous morphisms of sites ...
González, Julia Ramos
core   +1 more source

Presenting a Category Modulo a Rewriting System [PDF]

, 2015
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the
Clerc, Florence, Mimram, Samuel
core   +4 more sources

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization [PDF]

, 2011
In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be ...
Auslander M., Cohn P. M., Cox D. A., Decker W., Gago-Vargas J., Greuel G.-M., Greuel G.-M., Laubenbacher R. C., Mac Lane S., MARKUS LANGE-HEGERMANN, MOHAMED BARAKAT, Stafford J. T.   +11 more
core   +1 more source

Minimal resolutions and other minimal models [PDF]

, 1993
In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories . This equivalence follows from an axiomatic definition of minimal objects.
Roig, Agustí
core   +2 more sources