We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead productsâ€¦ (More)

In the general setting of groupoid enriched categories, notions of suspender and looper of a map are introduced, formalizing a generalization of the classical homotopy-theoretic notions of suspensionâ€¦ (More)

We introduce theories in which suspension, resp. loop objects, are defined and we describe the cohomology of such theories. Cohomology classes in degree 3 classify track theories. 2000 Mathematicsâ€¦ (More)

In the classical paper [A-H] Adams-Hilton constructed a free chain algebra which is an important algebraic model of a simply connected homotopy type. We show that this chain algebra (endowed with anâ€¦ (More)

Applicable Algebra in Engineering, Communicationâ€¦

2014

It is well-known how to compute the structure of the second homotopy group of a space, $$X$$ X , as a module over the fundamental group, $$\pi _1X$$ Ï€ 1 X , using the homology of the universal coverâ€¦ (More)

We show that the homotopy category of products of Z/p-Eilenbergâ€“Mac Lane spaces is an -algebra which algebraically is determined by the Steenrod algebra considered as a Hopf algebra with unstableâ€¦ (More)