Changes between Initial Version and Version 1 of Ticket #13400, comment 26


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Timestamp:
08/27/12 07:23:17 (7 years ago)
Author:
SimonKing
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  • Ticket #13400, comment 26

    initial v1  
    3939Actually I have wondered about that, myself. I guess it is just a tribute to very old code. IIRC, someone (William Stein?) argued as follows: It is actually typical that coercion goes from "less structure / simpler" (e.g. from a base ring) to "more structure / more complicated" (e.g., to a polynomial ring or to a matrix space over the base ring).
    4040
    41 And: If we have an object O in some category (say, GF(5) in the category of fields), and an object X that is obtained from O by a forgetful functor (say, Integers(5) in the category of fields), and we have a in O and b in X, then we typically want that a+b belongs to the "richer" structure - otherwise, we would have worked in X right away.
     41And: If we have an object O in some category (say, GF(5) in the category of fields), and an object X that is obtained from O by a forgetful functor (say, Integers(5) in the category of rings), and we have a in O and b in X, then we typically want that a+b belongs to the "richer" structure - otherwise, we would have worked in X right away.