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There is an excellent translation of the French article presenting the Benabou-Roubaud Theorem to English by Zoran Skoda which he certainly will provide on request.

On p.101 of https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/FiBo.pdf you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud.

The relation between this original formulation and the now common one can be found in Prop.4.5 of https://arxiv.org/pdf/math/0412512v4.pdf , i.e. Vistoli's excellent "Notes on Grothendieck topologies, fibered categories and descent theory".

There is an excellent translation of the French article presenting the Benabou–Roubaud Theorem to English by Zoran Škoda which he certainly will provide on request.

On p.101 of Fibered Categories (à la Jean Bénabou) you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud.

The relation between this original formulation and the now common one can be found in Prop.4.5 of Vistoli's excellent Notes on Grothendieck topologies, fibered categories and descent theory (arXiv:math/0412512).

There is an excellent translation of the French article presenting the Benabou-Roubaud Theorem to English by Zoran Skoda which he certainly will provide on request.

On p.101 of https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/FiBo.pdf you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud

There is an excellent translation of the French article presenting the Benabou-Roubaud Theorem to English by Zoran Skoda which he certainly will provide on request.

On p.101 of https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/FiBo.pdf you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud.

The relation between this original formulation and the now common one can be found in Prop.4.5 of https://arxiv.org/pdf/math/0412512v4.pdf , i.e. Vistoli's excellent "Notes on Grothendieck topologies, fibered categories and descent theory".

There is an excellent translation of the French article presenting the Benabou-Roubaud Theorem to English by Zoran Skoda whom he certainly will provide on request. On p.101 of https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/FiBo.pdf you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud

There is an excellent translation of the French article presenting the Benabou-Roubaud Theorem to English by Zoran Skoda which he certainly will provide on request.

On p.101 of https://www2.mathematik.tu-darmstadt.de/~streicher/FIBR/FiBo.pdf you find the original definition of descent maps in terms of fibrations due to Grothendieck and Giraud