higher groupslong exact sequenceWorking in homotopy type theory, we introduce the notion of n-exactness for a short sequence F→E→Bof pointed types and show that any fiber sequence F(→)E(→)B of arbitrary types induces a short sequence‖F‖_(n?1)→‖E‖_(n?1)→‖B‖_(n?1)that...
Thus the homology groups can be used to distin- guish between topological spaces; if the homology groups differ, the spaces cannot be homeomorphic.] Note that any exact sequence is a complex, since the composition of successive maps is 0. 1 2 S1.2 Definition A chain map f : C ...
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 -...
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...
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), ...
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 ......
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...