Subject: categories: Answer to Charles Wells

From: Andree Ehresmann <[email-masked]>
Date: Wed, 12 Jul 2000 18:45:46 +0200

In answer to Charles Wells
>Can anyone tell me what Ehresmann meant by a "saturated functor" 
>(foncteur saturé) in 1967?

Charles Ehresmann defined a "homomorphism saturated functor" 
already in his lectures in 1962, and it figures in his 1963 paper
"Categories structurees" (Annales ENS), reprinted in

"Charles Ehresmann: Oeuvres completes et Commentees", Part III-1, Amiens
1980, p. 29 

In the "Comments" in this book I have given English translations in more
modern terms of the main categorical definitions and results of Charles,
which, up to the seventies, were often written in a non-usual style, very
difficult to decipher to-day (and even at that moment for most readers,
which explains they were not as widely known as they should have been!)
In particular in the Note 29-2 (p. 348-9 of this book) I have translated
the definition in more modern terms:

A "homomorphism saturated functor" p: H -> C is a faithful amnestic functor
which creates isomorphisms; amnestic means that an isomorphism mapped on an
identity is an identity. Thus H is a concrete category over C, such that
the restriction of p to the groupoid of isomorphisms of H is a discrete
op-fibration.

(there are more information in this Note).