This statement concerns the resemblance of [DW], the recently
"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
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
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
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