Denecke, Klaus; Wismath, Shelly L.:

Universal algebra and coalgebra.

Hackensack, NJ: World Scientific, ISBN 978-981-283-745-5/hbk (2009; Zbl review).

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