LEADER 04159nam 22007213 450 001 9910972378803321 005 20231110225030.0 010 $a9781470467494 010 $a1470467496 035 $a(CKB)4940000000616159 035 $a(MiAaPQ)EBC6798085 035 $a(Au-PeEL)EBL6798085 035 $a(RPAM)22495357 035 $a(PPN)25997160X 035 $a(OCoLC)1275392905 035 $a(EXLCZ)994940000000616159 100 $a20211214d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGoodwillie Approximations to Higher Categories 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (126 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.272 300 $a"July 2021, volume 272, number 1333 (third of 7 numbers)." 311 08$a9781470448936 311 08$a1470448939 320 $aIncludes bibliographical references. 327 $aMain results -- Constructing n-excisive approximations -- Another construction of polynomial approximations -- Coalgebras in stable [infinity]-operads -- The space of Goodwillie towers -- Examples. 330 $a"We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More generally, we construct such a tower for a large class of -categories C and classify such Goodwillie towers in terms of the derivatives of the identity functor of C. As a particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p-local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching's spectral version of the Lie operad. This is a close analogue of Quillen's results on rational homotopy"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aHomotopy groups 606 $aAlgebraic topology 606 $aSpectral sequences (Mathematics) 606 $aClass field towers 606 $aAlgebraic topology -- Homotopy theory -- None of the above, but in this section$2msc 606 $aAlgebraic topology -- Homotopy theory -- Classification of homotopy type$2msc 606 $aAlgebraic topology -- Homotopy theory -- Homotopy functors$2msc 606 $aAlgebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory$2msc 606 $aAlgebraic topology -- Applied homological algebra and category theory -- Topological categories, foundations of homotopy theory$2msc 615 0$aHomotopy groups. 615 0$aAlgebraic topology. 615 0$aSpectral sequences (Mathematics) 615 0$aClass field towers. 615 7$aAlgebraic topology -- Homotopy theory -- None of the above, but in this section. 615 7$aAlgebraic topology -- Homotopy theory -- Classification of homotopy type. 615 7$aAlgebraic topology -- Homotopy theory -- Homotopy functors. 615 7$aAlgebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory. 615 7$aAlgebraic topology -- Applied homological algebra and category theory -- Topological categories, foundations of homotopy theory. 676 $a514/.24 686 $a55P99$a55P15$a55P65$a55U35$a55U40$2msc 700 $aHeuts$b Gijs$01255141 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910972378803321 996 $aGoodwillie Approximations to Higher Categories$94344985 997 $aUNINA