- Fibrant object
In
mathematics , specifically inhomotopy theory in the context of amodel category "M", a fibrant object "A" of "M" is an object that has afibration to theterminal object of the category.Properties
The fibrant objects of a
closed model category are characterized by having a right lifting property with respect to any trivial cofibration in the category. This property makes fibrant objects the "correct" objects on which to definehomotopy group s. In the context of the theory ofsimplicial set s, the fibrant objects are known as Kan complexes afterDaniel Kan .References
*P.G. Goerss and J.F. Jardine, "Simplicial Homotopy Theory", Progress in Math., Vol. 174, Birkhauser, Boston-Basel-Berlin, 1999. ISBN 3-7643-6064-X.
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