mathematics, the Puppe sequence is a construction of homotopy theory, so named after Dieter Puppe. It comes in two forms: a long exact sequence, built from...

cofibration, there also exists a sequence of cofibrations. These two sequences are known as the Puppe sequences or the sequences of fibrations and cofibrations...

mapping cone, then the resulting exact (or dually, coexact) sequence is given by the Puppe sequence. There are many realizations of spheres as homogeneous...

known for the Puppe sequence in algebraic topology. Dieter Puppe was born the son of the lawyer Siegmund Puppe. The mathematician Volker Puppe (born 1938)...

Georg Puppe (1867–1925) was a German social physician and medical examiner. Georg Puppe attended the Raths- and Friedrichs-Gymnasium in Kostrzyn nad Odrą...

cones are famously used to construct the long coexact Puppe sequences, from which long exact sequences of homotopy and relative homotopy groups can be obtained...

morphism of their long exact sequences of homotopy groups, from which (by applying the Five Lemma, as is done in the Puppe sequence) one can see that the map...

is a space over X through a projection. Puppe sequence The Puppe sequence refers ro either of the sequences X → f Y → C f → Σ X → Σ Y → ⋯ , {\displaystyle...

which in turn leads to the duality of the long exact and coexact Puppe sequences. In homological algebra, the relationship between currying and uncurrying...

\,} and more generally, the duality between the exact and coexact Puppe sequences. This also allows us to relate homotopy and cohomology: we know that...