04159nam 22007213 450 991097237880332120231110225030.097814704674941470467496(CKB)4940000000616159(MiAaPQ)EBC6798085(Au-PeEL)EBL6798085(RPAM)22495357(PPN)25997160X(OCoLC)1275392905(EXLCZ)99494000000061615920211214d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierGoodwillie Approximations to Higher Categories1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (126 pages)Memoirs of the American Mathematical Society ;v.272"July 2021, volume 272, number 1333 (third of 7 numbers)."9781470448936 1470448939 Includes bibliographical references.Main results -- Constructing n-excisive approximations -- Another construction of polynomial approximations -- Coalgebras in stable [infinity]-operads -- The space of Goodwillie towers -- Examples."We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More generally, we construct such a tower for a large class of -categories C and classify such Goodwillie towers in terms of the derivatives of the identity functor of C. As a particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p-local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching's spectral version of the Lie operad. This is a close analogue of Quillen's results on rational homotopy"--Provided by publisher.Memoirs of the American Mathematical Society Homotopy groupsAlgebraic topologySpectral sequences (Mathematics)Class field towersAlgebraic topology -- Homotopy theory -- None of the above, but in this sectionmscAlgebraic topology -- Homotopy theory -- Classification of homotopy typemscAlgebraic topology -- Homotopy theory -- Homotopy functorsmscAlgebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theorymscAlgebraic topology -- Applied homological algebra and category theory -- Topological categories, foundations of homotopy theorymscHomotopy groups.Algebraic topology.Spectral sequences (Mathematics)Class field towers.Algebraic topology -- Homotopy theory -- None of the above, but in this section.Algebraic topology -- Homotopy theory -- Classification of homotopy type.Algebraic topology -- Homotopy theory -- Homotopy functors.Algebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory.Algebraic topology -- Applied homological algebra and category theory -- Topological categories, foundations of homotopy theory.514/.2455P9955P1555P6555U3555U40mscHeuts Gijs1255141MiAaPQMiAaPQMiAaPQBOOK9910972378803321Goodwillie Approximations to Higher Categories4344985UNINA