Deriving calculus with cotriples

DOI10.1090/S0002-9947-03-03318-XzbMath1028.18004MaRDI QIDQ4433116

Brenda Johnson, Randy McCarthy

Publication date: 29 October 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Taylor towercotripleQ-constructionsstable derived functions

Mathematics Subject Classification ID

Chain complexes in algebraic topology (55U15) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Homotopy functors in algebraic topology (55P65) Algebraic (K)-theory of spaces (19D10)

Related Items

André--Quillen spectral sequence for \(THH\)., Derived Koszul duality and \(\mathsf{TQ}\)-homology completion of structured ring spectra, A simplicial foundation for differential and sector forms in tangent categories, Unnamed Item, Enriched functor categories for functor calculus, Groupes d’extensions et foncteurs polynomiaux, Unnamed Item, A functorial control of integral torsion in homology, Linearizing Combinators, HKR theorem for smooth \(S\)-algebras., Homotopy completion and topological Quillen homology of structured ring spectra, The rank filtration and Robinson's complex, Directional derivatives and higher order chain rules for abelian functor calculus, Localisation homotopique et tour de Taylor pour une catégorie abélienne, Taylor towers for \(\Gamma\)-modules, Algebraic Goodwillie calculus and a cotriple model for the remainder, Functional equations and their related operads, Splitting criteria for homotopy functors of spectra, Cross effects and calculus in an unbased setting, Finitude homologique des foncteurs sur une catégorie additive et applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homologie nicht-additiver Funktoren. Anwendungen
• The free loop space and the algebraic K-theory of spaces
• Calculus. II: Analytic functors
• Taylor towers for functors of additive categories
• The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres
• Relative algebraic \(K\)-theory and topological cyclic homology
• Calculus. III: Taylor series
• An Atiyah-Hirzebruch spectral sequence for topological André-Quillen homology
• \(\Gamma\)-homology, topological André-Quillen homology and stabilization
• The Taylor towers for rational algebraic \(K\)-theory and Hochschild homology
• Calculus. I: The first derivative of pseudoisotopy theory
• André--Quillen spectral sequence for \(THH\).
• Homotopical algebra
• Cohomology of algebraic theories
• The Mitchell-Richter filtration of loops on Stiefel manifolds stably splits
• Stable derived functors, the Steenrod algebra and homological algebra in the category of functors
• Algebraic Goodwillie calculus and a cotriple model for the remainder
• Stable derived functors of the second symmetric power functor, second exterior power functor and Whitehead gamma functor
• Linearization, Dold-Puppe stabilization, and Mac Lane’s 𝑄-construction
• Orthogonal Calculus
• Homology Theories for Multiplicative Systems