This statement concerns the resemblance of [DW], the recently
published book
"Universal Algebra and Coalgebra" by K. Denecke
and S. Wismath [Hackensack, NJ:
World Scientific
(2009; Zbl 1176.08001)],
to [G], the text "Universelle Coalgebra"
by H. P. Gumm, which was published as
an appendix to the book "Allgemeine Algebra"
by
Th. Ihringer [Berliner Studienreihe zur Mathematik 10; Lemgo: Heldermann Verlag
(2003; Zbl 1036.08001)].
The resemblance between the two texts, at each level of
organisation, is
striking. [DW] contains 12 chapters, of which the
chapters 2,3,4,7,8 and 9
are about coalgebra. Of these, all but
the last one are completely based
on [G], in the following
sense:
1 At the level of overall organisation, the table of
contents
of these chapters is virtually the same as that of [G].
2
Individual chapters of [DW] are organized in almost
the same manner
as the corresponding sections of [G]. For instance,
(a) In
chapter 2 of [DW] all 11 sections but 2.5 and 2.9 correspond
one-to-one to the sections of Section 1.1 - 1.8 of [G];
(b) Modulo some minor reorganisation, the 10 sections of chapter 4 of
[DW]
directly correspond to the
sections 3.0 - 3.8 of [G];
(c) Chapter 7 of [DW] follows
the build-up of the sections 4.1-4.4 of [G];
(d) Chapter 8
that of 4.5-4.7.
3 At the level of sections, the authors of [DW]
in a number of cases copy
the structure of the
corresponding parts of [G]; to name just a few:
(a) the
sections 4.3 and 4.4 of [DW] are clear copies of section 3.2 in
[G];
(b) the sections 2.1-2.4 and 2.6-2.8 of [DW] are clear
copies of the
sections 1.1-1.7 of
[G]
4 At the level of paragraphs, a large part of the text of [DW]
consists of
sentence by sentence translation of material
from [G]; for example: pages
48-50 in [DW] are translations
of the corresponding text of pages 166-168
of [G].
5 At
the level of individual examples, notation, etc it becomes even
more
clear to which degree the material on coalgebra in
[DW] is taken from [G]:
most of the names of variables,
most diagrams, etc., in [DW] are exactly
as in [G].
Note
that [G] is not cited as a source for [DW]. The only credits to [G]
are
given for Lemma 4.1.4 and for (an insignificant) Lemma
7.5.2.
Summarizing, we can describe the mentioned chapters of
[DW] as
the translated version of [G], with minor modifications,
and
reorganizations of the material. There can be no doubt
whatsoever
that the intellectual ownership of the material resides
with H. Peter Gumm.
Jiri Adamek, Jan Rutten and Yde Venema