The following "fundamental construction" is mentioned in Bart Jacobs's thesis, from which we can derive a few useful fibrations

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I have some blind spot ironing everything out, and wanted to look up some other references about it.

Does this construction have a name ?

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    $\begingroup$ I don't know of a name for it that you'll be able to look up (I've never seen it anywhere but Jacobs' book), but if I had to call it something I'd probably call it a "fiberwise simple fibration", since on each fiber of E it is the usual simple fibration. $\endgroup$ – Mike Shulman Jun 18 '17 at 15:59
  • $\begingroup$ that's good to know and something to ponder. thank you ! $\endgroup$ – nicolas Jun 18 '17 at 22:29

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