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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction............................................................................................................ 5
Chapter I. PRELIMINARIES
1. Notation. Categories and functors................................................................ 8
2. Concrete categories................................................................................................ 12
3. Power functors. Set-theoretical lemmas............................................................. 16
4. The category of equivalence relations................................................................. 19
5. Pseudo-reflections and reflections...................................................................... 20
6. Universal points. Generators and cogenerators................................................ 21
Chapter II. DUALITY. GENERALIZED EMBEDDINGS AND QUOTIENTS
7. Dual notions in concrete categories........................................................... 23
8. D-preorders and C-preorders............................................................................... 27
9. Generalized images, coimages, embeddings and quotients........................ 33
Chapter III. THE CONDITIONS OF TRANSFER AND OF UNICITY
10. Definitions, examples, and basic properties.......................................... 38
11. The "transfer" functor ........................................................................................... 42
12. The "unicity" functor............................................................................................... 44
13. The "unique transfer" functor............................................................................... 46
14. Structures and concrete categories................................................................... 48
Chapter IV. THE CATEGORY OF LOGICAL KITS
15. Definitions and basic properties................................................................ 51
16. Adjoints of some forgetful functors.................................................................... 55
17. Coproducts of logical kits.................................................................................... 58
18. Coequalizers in the category of logical kits...................................................... 61
References .......................................................................................................... 64
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
135
Liczba stron
65
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXXXV
Daty
wydano
1976
Twórcy
autor
Bibliografia
- [1971] M. Barr, P. A. Grillet and D. H. Osdol, Exact categories and categories of sheaves, Lecture Notes in Mathematics 236, Berlin 1971.
- [1966] H.-B. Brinkmann and D. Puppe, Kategorien und Funktoren, Lecture Notes in Mathematics 18, Berlin 1966.
- [1968] I. Bucur and A. Deleanu, Introduction to the theory of categories and functors, London-New York-Sydney 1968.
- [1969] M. S. Calenko, Representations of concrete categories in the category of sets (Russian.), Mat. Zametki 6 (1969), p. 125-127.
- [1957] C. Ehresmann, Gattungen von lokalen Strukturen, Jahresbericht der Deutschen Mathematiker-Verein 60 (1957), p. 49-77.
- [1972] H. Ehrig and M. Pfender, Kategorien und Automaten, Berlin-New York 1972.
- [1942] S. Eilenberg and S. MacLane, Natural isomorphisms in group theory, Proc. Nat. Acad. Sci. U. S. A. 28 (1942), p. 537-543.
- [1945] S. Eilenberg, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), p. 231-294.
- [1968] R. Engelking, Outline of.general topology, Warszawa 1968.
- [1964] P. Freyd, Abelian categories, New York 1964.
- [1970] P. Freyd Homotopy is not concrete, The Steenrod algebra and its applications, Lecture Notes in Mathematics 168 (1970), p. 25-34.
- [1970] V. S. Garvackiï and B. M. Šaĭn, Injective and surjective morphisms in abstract categories (Russian.), Colloq. Math. 22 (1970), p. 51-57.
- [1957] A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. (2) 9 (1957), p. 119-221.
- [1968] H. Herrlich, Topologische Reflexionen und Goreflexionen, Lecture Notes in Mathematics 78, Berlin 1968.
- [1973] H. Herrlich and G. E. Strecker, Category theory, Boston 1973.
- [1957] J. R. Isbell, Some remarks concerning categories and subspaces, Canadian J. Math. 9 (1957), p. 563-577.
- [1958] J. R. Isbell, Algebras of uniformly continuous functions, Ann. of Math. 68 (1958), p. 96-125.
- [1963] J. R. Isbell, Two set-theoretical theorems in categories, Fund. Math. 53 (1963), p. 44-49.
- [1964] J. R. Isbell, Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat. 36, Warszawa 1964.
- [1972] L. Kučera, and A. Pultr, On a mechanism of defining morphisms in concrete categories, Cahiers Topologie Géom. Différentielle 13 (1972), p. 397-410.
- [1960] A. G. Kuroš, A. H. Livšic, and E. G. Šulgeĭfer, Foundations of the theory of categories, English translation in Russian Mathematical Surveys from Uspehi Matematiceskih Nauk 15 (1960), No. 6, p. 3-52.
- [1950] S. MacLane, Duality for groups, Bull. Amer. Math. Soc. 56 (1950), p. 485-516.
- [1972] S. MacLane, Categories for the working mathematician, Berlin 1972.
- [1967] S. MacLane, and G. Birkhoff, Algebra, New York 1967.
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