HOMOTOPY groupsWorking in homotopy type theory, we introduce the notion of n -exactness for a short sequence $Fo Eo B$ of pointed types and show that any fiber sequence $F\\hookrightarrow E woheadrightarrow B$ of arbitrary types induces a short sequence that is n -exact at $\...
category of compactly generated weak hausdorff spaces. using this, we compute the first page of the integral bousfield–kan homotopy spectral sequence of the tower of fibrations, given by the taylor tower of the embedding functor associated to the space of long knots. based on the methods in ...
30 Ryomei Iwasa - 33 Motivic Stable Homotopy Theory 1:19:41 Ana Caraiani - On the cohomology of Shimura varieties with torsion coefficients 1:11:59 Souvenirs d'Alexander Grothendieck par Michel Demazure 06:53 Savant Mélange Cédric Villani - D'où viennent les idées 19:28 Dustin Clausen -...
general case when η may be non-exact. Unfortunately, compactness as stated above may then fail. (A simple class of counter-examples is described after Theorem 1.4 below.) It is then natural to seek topological conditions which ensure that compactness does hold. We will consider two approaches...
Theorem B gives another useful sufficient condition for homotopy equivalence, and its application is sketched for the Localization Theorem and the consequent long exact sequence of Kgroups. Example applications include \\(K_n A\\cong K_n~A[T]\\) and \\(K_n~A[T, T^{-1}]\\cong K_n...
Afterwards, Bourn also obtained a long exact cohomology sequence in =-=[4]-=- by using internal n-groupoids. The cohomology groups HnE(A) are defined through internal (n − 1)-groupoids for which there is an internal n-functor from its induced indiscrete internal n-groupoid to ......
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University of GranadaA. Cegarra and A. Garzon, A long exact sequence in non-abelian cohomology, Lecture Notes in Math., Springer-Verlag, 1488 (1991), 79-94.A.Cegarra and A.Garzon, A long exact sequence in non-abelian cohomology, Lecture Notes in Math., Springer-Verlag, 1488 (1991), ...
R. Garzon, A long exact sequence in non-abelian cohomology, in: Category Theory (Como, 1990), pp. 79-94, Lecture Notes in Mathematics 1488, Springer-Verlag, Berlin, 1991.A. Cegarra and A. Garzon, A long exact sequence in non-abelian cohomology. Lecture Notes in Math. 1488(1991), 79...