* Answer to Charles Wells
@ 2000-07-12 16:45 Andree Ehresmann
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From: Andree Ehresmann @ 2000-07-12 16:45 UTC (permalink / raw)
To: categories
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).
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