Subject: categories: More about names and notation

From: "David B. Benson" <[email-masked]>
Date: Tue, 28 Nov 2000 12:51:18 -0800

Dear Colleagues,

Thank you for the responses!

(1) Several pointed out that my <<followers>> relations are
    said to be <<covering>> relations in combinatorics.
    These relations are defined as relations which are
      1. acyclic
      2. without interpolants, as Robert Dawson mentioned.
    A followers relation for discrete partial order R is
    the least relation whose reflexive and transitive closure
    is R.
       This agrees entirely with the definition of a
    successor relation being the least relation whose
    transitive closure is a discrete strict total order and whose
    reflexive and transitive closure is a discrete total order.
       In the case of successor, there is a distinct
    next element, as in the succession of the Kings (and Queens)
    of England.  In the case of followers, there is in
    general a set of next elements, such as the followers
    of Cromwell.

(2) While several alternatives were offered, I will try
    Paul Taylor's <<instance>> of a relation to describe
    an ordered pair (x,y) \in R.

(3) The problem of a good name for the sets Nat_k remains.
    Suggestions included
      finite ordinals
      numerals
      order ideals
    and by far the most appropriate for my purposes,
      index sets
    [This problem of a good name is worthy of some further attention.
     Computer science second year students will think 
       of <<finite ordinals>> as a number, not a set,
       of <<numerals>> as representations of the digits in a number system,
     and have not be exposed to order ideals.]

Cheers,
David
--
Professor David B. Benson                                (509) 335-2706
School of EE and Computer Science (EME 102A)             (509) 335-3818 fax
PO Box 642752, Washington State University               [email-masked]
Pullman WA 99164-2752   U.S.A.