McCarthy, Randy Dual calculus for functors to spectra. (English) Zbl 0996.19005 Greenlees, J. P. C. (ed.) et al., Homotopy methods in algebraic topology. Proceedings of an AMS-IMS-SIAM joint summer research conference, University of Colorado, Boulder, CO, USA, June 20-24, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 271, 183-215 (2001). Author’s abstract: We construct a theory formally dual to Goodwillie’s calculus of functors for functors which take values in spectra. We then show that the two theories are essentially equivalent for endofunctors of spectra when particular obstruction groups obtained from Tate cohomology vanish. We apply this fact to show that a particular coTower for rational algebraic \(K\)-theory is as effective but no more effective than its dual counterpart – negative cyclic homology.For the entire collection see [Zbl 0964.00013]. Reviewer: U.Tillmann (Oxford) Cited in 3 ReviewsCited in 13 Documents MSC: 19D55 \(K\)-theory and homology; cyclic homology and cohomology 55P42 Stable homotopy theory, spectra 18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects) Keywords:negative cyclic homology; endofunctors of spectra; Tate cohomology PDFBibTeX XMLCite \textit{R. McCarthy}, Contemp. Math. 271, 183--215 (2001; Zbl 0996.19005)