(Infinity, 2)-Categories and the Goodwillie Calculus I
J Lurie - arXiv preprint arXiv:0905.0462, 2009 - arxiv.org
The bulk of this paper is devoted to the comparison of several models for the theory of
(infinity, 2)-categories: that is, higher categories in which all k-morphisms are invertible for k> …
(infinity, 2)-categories: that is, higher categories in which all k-morphisms are invertible for k> …
[图书][B] Cubical homotopy theory
BA Munson, I Volić - 2015 - books.google.com
Graduate students and researchers alike will benefit from this treatment of classical and
modern topics in homotopy theory of topological spaces with an emphasis on cubical …
modern topics in homotopy theory of topological spaces with an emphasis on cubical …
Operads and chain rules for the calculus of functors
G Arone, M Ching - arXiv preprint arXiv:0902.0399, 2009 - arxiv.org
We study the structure possessed by the Goodwillie derivatives of a pointed homotopy
functor of based topological spaces. These derivatives naturally form a bimodule over the …
functor of based topological spaces. These derivatives naturally form a bimodule over the …
[HTML][HTML] Stable homotopy of algebraic theories
S Schwede - Topology, 2001 - Elsevier
The simplicial objects in an algebraic category admit an abstract homotopy theory via a
Quillen model category structure. We show that the associated stable homotopy theory is …
Quillen model category structure. We show that the associated stable homotopy theory is …
Goodwillie calculus
G Arone, M Ching - Handbook of homotopy theory, 2020 - taylorfrancis.com
Goodwillie calculus is a method for analyzing functors that arise in topology. One may think
of this theory as a categorification of the classical differential calculus of Newton and …
of this theory as a categorification of the classical differential calculus of Newton and …
[PDF][PDF] Derived algebraic geometry vi: E_k algebras
J Lurie - arXiv preprint arXiv:0911.0018, 2009 - arxiv.org
arXiv:0911.0018v1 [math.AT] 30 Oct 2009 Page 1 arXiv:0911.0018v1 [math.AT] 30 Oct 2009
Derived Algebraic Geometry VI: E[k]-Algebras May 29, 2018 Contents 1 Foundations 5 1.1 …
Derived Algebraic Geometry VI: E[k]-Algebras May 29, 2018 Contents 1 Foundations 5 1.1 …
Stable infinity categories
J Lurie - arXiv preprint math/0608228, 2006 - arxiv.org
This paper is an expository account of the theory of stable infinity categories. We prove that
the homotopy category of a stable infinity category is triangulated, and that the collection of …
the homotopy category of a stable infinity category is triangulated, and that the collection of …
[HTML][HTML] Directional derivatives and higher order chain rules for abelian functor calculus
In this paper, we consider abelian functor calculus, the calculus of functors of abelian
categories established by the second author and McCarthy. We carefully construct a …
categories established by the second author and McCarthy. We carefully construct a …
A chain rule for Goodwillie derivatives of functors from spectra to spectra
M Ching - Transactions of the American Mathematical Society, 2010 - ams.org
We prove a chain rule for the Goodwillie calculus of functors from spectra to spectra. We
show that the (higher) derivatives of a composite functor $ FG $ at a base object $ X $ are …
show that the (higher) derivatives of a composite functor $ FG $ at a base object $ X $ are …
Tangent infinity-categories and goodwillie calculus
We make precise the analogy between Goodwillie's calculus of functors in homotopy theory
and the differential calculus of smooth manifolds by introducing a higher-categorical …
and the differential calculus of smooth manifolds by introducing a higher-categorical …