Homotopy Lifting Property
If we have a homotopy H : X × → Y and a cover p : Y → Y and we are given a map h0 : X → Y such that H0 = p ○ h0 (h0 is called a lift of h0), then we can lift all H to a map H : X × → Y such that p ○ H = H. The homotopy lifting property is used to characterize fibrations.
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Famous quotes containing the words lifting and/or property:
“O Westmoreland, thou art a summer bird,
Which ever in the haunch of winter sings
The lifting up of day.”
—William Shakespeare (1564–1616)
“Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)