Results 21 to 30 of about 2,632 (59)
The derived category with respect to a generator
, 2014 Consider a Grothendieck category $\mathcal{G}$ along with a choice of generator $G$, or equivalently a generating set $\{G_i\}$. We introduce the derived category $\mathcal{D}(G)$, which kills all $G$-acyclic complexes, by putting a suitable model ...
Gillespie, James
core +1 more source
Equivariant homotopy epimorphisms, homotopy monomorphisms and homotopy equivalences
Bulletin of the Belgian Mathematical Society - Simon Stevin, 1995 Let \(G\) be a finite group. Using Bredon-Illman cohomology with equivariant local coefficients systems conditions are given on a morphism in the \(G\)-homotopy category of pointed \(G\)-complexes to be an equivalence. In the case of the trivial group a variant of a result of \textit{E. Dyer} and \textit{J. Roitberg} [Topology Appl.
openaire +3 more sources
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
, 2007 We prove new upper bounds on homotopy and homology groups of o-minimal sets in terms of their approximations by compact o-minimal sets. In particular, we improve the known upper bounds on Betti numbers of semialgebraic sets defined by quantifier-free ...
Gabrielov, Andrei, Vorobjov, Nicolai
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Quillen model structures for relative homological algebra
, 2013 An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is encompassed by Quillen's
Christensen, J. Daniel, Hovey, Mark
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A criterion for existence of right-induced model structures
, 2019 Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when $F$ admits both
Drummond-Cole, Gabriel C. +1 more
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, 2021 We study several aspects of the study of Ind-Banach modules over Banach rings thereby synthesizing some aspects of homological algebra and functional analysis.
Ben-Bassat, Oren, Kremnizer, Kobi
core
Sato Grassmannians for generalized Tate spaces [PDF]
, 2010 We generalize the concept of Sato Grassmannians of locally linearly compact topological vector spaces (Tate spaces) to the category limA of the "locally compact objects" of an exact category A, and study some of their properties.
Previdi, Luigi
core
Pure braid groups are not residually free
, 2011 We show that the Artin pure braid group on at least four strands is not residually free.
Cohen, Daniel C. +2 more
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On the 3-arrow calculus for homotopy categories
, 2011 We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be embedded in a 3-
Thomas, Sebastian
core +1 more source