
We give necessary and sufficient conditions for a homotopy cartesian square to be homotopy cocartesian. Specializing, we obtain a necessary and sufficient condition for a fibration to be a cofibration. We apply the above to localization of spaces and to acyclic maps.
fibration, Fiber spaces in algebraic topology, Localization and completion in homotopy theory, cofibration, Homotopy extension properties, cofibrations in algebraic topology, Eckmann-Hilton duality, acyclic map
fibration, Fiber spaces in algebraic topology, Localization and completion in homotopy theory, cofibration, Homotopy extension properties, cofibrations in algebraic topology, Eckmann-Hilton duality, acyclic map
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