First quadrant spectral sequences in algebraic k-theory via homotopy colimits

DOI10.1080/00927878208822794zbMath0502.55012OpenAlexW1974003593MaRDI QIDQ3968168

Robert W. Thomason

Publication date: 1982

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927878208822794

zbMATH Keywords

spectral sequencesgroup completionsymmetric monoidal categoryhomotopy colimitspermutative categorycategory of spectradouble mapping cylinderfirst quadrant spectral sequences in algebraic K-theoryresolution by free symmetric monoidal categories

Mathematics Subject Classification ID

Spectral sequences, hypercohomology (18G40) Homotopy theory (55P99) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Spectral sequences in algebraic topology (55T99) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Homotopy functors in algebraic topology (55P65)

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Filtered spectra arising from permutative categories, Singularity theory and configuration space models of \(\Omega ^ nS^ n\) of non-connected spaces, Simplicial presheaves, Classifying Spaces for Foliations with Isolated Singularities, The homology of the Higman-Thompson groups, Deligne-Riemann-Roch and intersection bundles, The mathematical enterprises of Robert Thomason, Pairings of categories and spectra, Homotopy colimits of algebras over Cat-operads and iterated loop spaces, Brauer spaces for commutative rings and structured ring spectra, The period-index problem for twisted topological \(K\)-theory, A categorical context for the james-hopf maps, Supercoherence, \(KK\)-theories for topological algebras, \(G \)-theory of \(\mathbb F_1\)-algebras I: the equivariant Nishida problem, Hermitian \(K\)-theory of \(A_{\infty{}}\) rings. Homotopy invariance and the hyperbolic map, Hermitian \(K\)-theory on a theorem of Giffen, The linearisation map in algebraic K-theory, Geometric modules and algebraic \(K\)-homology theory, Cohomological obstruction theory for Brauer classes and the period-index problem, Algebraic K-Theory of ∞-Operads, Bar and cobar constructions. I, Geometric modules and Quinn homology theory

Cites Work

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• Uniqueness of delooping machines
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• Functors between tensored categories
• Coherence in closed categories
• The geometry of iterated loop spaces
• Homotopy limits, completions and localizations
• Higher algebraic K-theory: I
• Homotopy colimits in the category of small categories
• Fibrations and geometric realizations