fiberkategori
The fiber category, or fiberkategori, is a construction in category theory associated with a functor F: E -> B and a chosen object b in B. The fiber E_b is the comma category (F ↓ b). Its objects are pairs (e, φ) where e is an object of E and φ: F(e) -> b is a morphism in B. A morphism from (e, φ) to (e', φ') is a morphism f: e -> e' in E such that φ = φ' ∘ F(f). Intuitively, E_b collects all objects of E together with their structure maps to the base object b.
If F is a fibration, the fiber construction interacts with arrows in B. For a morphism u:
Relation to other concepts: The fiber E_b is the over-category (id_B ↓ b) when F is the identity
See also: comma category, over category, fibration, Grothendieck construction, descent.