Characterizations of Fibrations and Cofibrations By Lifting Properties
Cofibrations can be characterized as the maps which have the left lifting property with respect to acyclic fibrations, and acyclic cofibrations are characterized as the maps which have the left lifting property with respect to fibrations. Similarly, fibrations can be characterized as the maps which have the right lifting property with respect to acyclic cofibrations, and acyclic fibrations are characterized as the maps which have the right lifting property with respect to cofibrations.
Read more about this topic: Model Category
Famous quotes containing the words lifting and/or properties:
“Thales claimed that everything was water. He also put wine into water to sterilize it. Did he really believe he was putting water into water to sterilize it? Parmenides, like most Greeks, knew that wine was not water. But while lifting a glass of wine to his lips, he denied that motion was possible. Did he really believe that the glass was not moving when he lifted it?”
—Avrum Stroll (b. 1921)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)