CONTENTS
Chapter I. Introduction
0. General prerequisites 1
1. Introductory sketch - what are coalgebras, and why? 1
2. Overview of results 4
3. Results in the literature 6
4. Notes on this book; acknowledgements 7
Chapter II. Review of coalgebras and representable functors
5. Category-theoretic formulations of universal properties, and some
other matters 9
6. Basic definitions and results of universal algebra 18
7. Some conventions followed throughout this work 19
8. Algebra and coalgebra objects in a category, and representable
algebra-valued functors 20
9. Digressions on representable functors 30
Chapter III. Representable functors from rings to abelian groups
10. yt-Rings 35
11. Representable functors and pointed categories 39
12. Plans and preparations 41
13. Proof of the structure theorem for co-AbSemigp^ objects 47
14. Some immediate consequences 55
Chapter IV. Digressions on semigroups, etc.
15. Representable functors to AbBinar^ 61
16. Representable functors to abelian semigroups without neutral
element - easy results 63
17. Symmetry conditions, and cocommutativity 68
18. Application to AbSemigp-valued functors 74
19. Some observations and questions on rings of symmetric elements 78
20. Representable functors from Semigp^ to Semigp^ 82
21. Representable functors among varieties of groups and semigroups 89
22. Some related varieties: binars, heaps, and Mal'cev algebras 95
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