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020 a| 9781470448936q| (paperback);

020 z| 9781470467494q| (epub);

035 a| (WaSeSS)ssj0002593727;

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084 a| 55P99a| 55P15a| 55P65a| 55U35a| 55U402| msc;

100 1 a| Heuts, Gijs.?| UNAUTHORIZED;

245 10 a| Goodwillie approximations to higher categoriesh| [electronic resource] /c| Gijs Heuts.;

260 a| Providence, RI :b| American Mathematical Society,c| [2021];

300 a| xi, 108 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1333;

500 a| "July 2021, volume 272, number 1333 (third of 7 numbers).";

504 a| Includes bibliographical references.;

505 0 a| Main results -- Constructing n-excisive approximations -- Another construction of polynomial approximations -- Coalgebras in stable [infinity]-operads -- The space of Goodwillie towers -- Examples.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Homotopy groups.=| ^A58019;

650 0 a| Algebraic topology.=| ^A22632;

650 0 a| Spectral sequences (Mathematics)=| ^A56249;

650 0 a| Class field towers.=| ^A247428;

650 7 a| Algebraic topology -- Homotopy theory.2| msc;

650 7 a| Algebraic topology -- Homotopy theory -- Classification of homotopy type.2| msc;

650 7 a| Algebraic topology -- Homotopy theory -- Homotopy functors.2| msc;

650 7 a| Algebraic topology -- Applied homological algebra and category theory -- Abstract and axiomatic homotopy theory.2| msc;

650 7 a| Algebraic topology -- Applied homological algebra and category theory -- Topological categories, foundations of homotopy theory.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6798085;

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Goodwillie approximations to higher categories / Gijs Heuts.

Author/creator	Heuts, Gijs
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2021]
Description	xi, 108 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Homotopy groups. Algebraic topology. Spectral sequences (Mathematics) Class field towers.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1333
Contents	Main results -- Constructing n-excisive approximations -- Another construction of polynomial approximations -- Coalgebras in stable [infinity]-operads -- The space of Goodwillie towers -- Examples.
Abstract	"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.
General note	"July 2021, volume 272, number 1333 (third of 7 numbers)."
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022008014
ISBN	9781470448936 (paperback)
ISBN	(epub)

Goodwillie approximations to higher categories / Gijs Heuts.

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