On collapsing Calabi–Yau fibrations

Diagonal Fibrations Are Pointwise Fibrations

On the category of bisimplicial sets there are different Quillen closed model structures associated to various definitions of fibrations. In one of them, which is due to Bousfield and Kan and that consists of seeing a bisimplicial set as a simplicial object in the category of simplicial sets, fibrations are those bisimplicial set maps such that each of the induced simplicial set maps is a Kan f...

On Two Results about Fibrations

Let h., denote a reduced homology theory on the category of based spaces and let h, denote the corresponding extension to an unreduced homology theory on the category of unbased spaces given by h , ( X ) = h,(X+), where X+ denotes X with the addition of a disjoint basepoint. The following was proved by W. Chach61ski [2], using the elaborate machinery of 'cellular inequalities' developed by E. D...

Notes on Serre fibrations

Here the solid arrows represent maps that are given, and the problem is to find a map h commuting in the diagram. Usually the map i is an inclusion, and p is some kind of “bundle map” such as a local product. Note the special cases: (i) if i is an inclusion, E = A, and f = 1A, then the extension problem asks whether A is a retract of X; and (ii) if p is surjective, X=B, and g = 1B, the lifting ...

On Stallings Fibrations

On Collapsing Narrowing