# homotopy lifting property

A map $f:X\to Y$ satisfies the homotopy lifting property if given any space $A$ and a map $g:A\to X$ and a homotopy $h$ of $f\circ g$, we have a homotopy $h^{\prime}$ of $g$, satisfying $f\circ h^{\prime}=h$.

 Title homotopy lifting property Canonical name HomotopyLiftingProperty Date of creation 2013-03-22 15:38:01 Last modified on 2013-03-22 15:38:01 Owner whm22 (2009) Last modified by whm22 (2009) Numerical id 6 Author whm22 (2009) Entry type Definition Classification msc 55R65 Related topic fibremap Related topic FibreBundle Related topic LocallyTrivialBundle Related topic LongExactSequenceLocallyTrivialBundle Related topic fibration Related topic homotopyextensionproperty Defines homotopy lifting property