Colimit theorems for relative homotopy groups
نویسندگان
چکیده
منابع مشابه
Colimit Theorems for Relative Homotopy Groups
The first paper [10] (whose results were announced in [8]) developed the necessary ‘algebra of cubes’. Categories G of ω-groupoids and C of crossed complexes were defined, and the principal result of [10] was an equivalence of categories γ : G → C. Also established were a version of the homotopy addition lemma, and properties of ‘thin’ elements, in an ω-groupoid. In particular it was proved tha...
متن کاملOn Relative Homotopy Groups of Modules
In his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the existing theorems in algebraic topology. First, we discover that one can study relative homotopy groups, of modules, from a viewpoint which is close...
متن کاملHomotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups
If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z is Map∗(EK+, Z) K , the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X is often given by (HG,X), where HG,X is a certain explicit construction given by a homotopy limit in the category of discrete G-spectra. Thus, in each of two common equi...
متن کاملExtraordinary Homotopy Groups
In this talk, we’ll introduce the field of chromatic homotopy theory, which is where all the major advancements on the πS ∗ problem have come from in the past 30+ years. Our express goal will be to study the Picard groups of the K(n)-localized stable categories, but to even make sense of that we’ll have to go on a fairly deep safari through chromatic homotopy. Technical aspects will be mostly k...
متن کاملHomotopy Nilpotent Groups
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1981
ISSN: 0022-4049
DOI: 10.1016/0022-4049(81)90080-3