Vol. 24, No. 2, 1968

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Some applications of a property of the functor Ef

Myles Tierney

Vol. 24 (1968), No. 2, 401–411

The functors mapping cone, Cf, and its dual, Ef, whose definitions will be recalled below, seem to have been introduced by Puppe and Nomura in 1958 and 1960 respectively. There, various basic properties of these functors were established. Here we shall prove a ‘3 × 3 lemma” for the functor Ef (with an obvious dual for Cf). This will be applied in §3 to the problem of determining a Postnikov system for Ef in terms of f, and to show that any space having a Postnikov decomposition, and whose homotopy is finitely generated, has a decomposition in which the only K(π,n)’s appearing have π a finitely generated free abelian group.

Mathematical Subject Classification
Primary: 55.50
Received: 1 June 1966
Published: 1 February 1968
Myles Tierney