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Lax descent theorems for left exact categories

Seria
Rozprawy Matematyczne tom/nr w serii: 346 wydano: 1995
Zawartość
Warianty tytułu
Abstrakty
EN
Abstract
We study the 2-category of categories with finite limits, Lex. We characterise descent, effective descent and chain descent morphisms. These classes of morphisms do not coincide in Lex. We also study relations between these and other naturally arising classes of conservative morphisms. We define, in a semantical way, a new false quotient-strongly conservative factorisation in Lex. We prove that the iteration of the descent construction eventually "stops" at this factorisation. This gives a syntactic description of the factorisation.
EN
CONTENTS
0. Introduction.........................................................................................5
1. Basic notions......................................................................................6
 1.1. Effective descent morphisms..........................................................7
 1.2. Left exact categories......................................................................9
 1.3. Factorisations in Lex.....................................................................11
 1.4. Descent theorem for exact categories..........................................16
2. The exact completion of the left exact categories.............................17
3. A characterisation of the descent category......................................24
4. A characterisation of the effective descent morphisms in Lex..........30
5. Some further results.........................................................................34
6. The false quotient-strongly conservative factorisation in Lex...........36
7. Conservative morphisms in Lex........................................................44
References...........................................................................................51
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 346
Liczba stron
55
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXLVI
Daty
wydano
1995
otrzymano
1992-05-08
poprawiono
1994-08-28
Twórcy
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland, zawado@mimuw.edu.pl
Bibliografia
  • [EC] M. Barr, Exact categories, in: Lecture Notes in Math. 236, Springer, 1971, 1-120.
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  • [CM] A. Carboni and R. Celia Magno, The free exact category on a left exact one, J. Austral. Math. Soc. Ser. A 33 (1982), 295-301.
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  • [FK] P. J. Freyd and G. M. Kelly, Categories of continuous functors, I, J. Pure Appl. Algebra 2 (1972), 169-191.
  • [GU] P. Gabriel und F. Ulmer, Lokal präsentierbare Kategorien, Lecture Notes in Math. 221, Springer, 1971.
  • [SGA1] A. Grothendieck, Revêtements Étales et Groupe Fondamental, Lecture Notes in Math. 224, Springer, 1971.
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  • [CWM] S. MacLane, Categories for the Working Mathematician, Springer, 1971.
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  • [MM1] M. Makkai, Duality and definability in first order logic, Mem. Amer. Math. Soc. 503 (1993).
  • [CWL] M. Makkai, Ultraproducts and categorical logic, in: Lecture Notes in Math. 1130, Springer, 1985, 222-309.
  • [MP] M. Makkai and R. Paré, Accessible Categories : The Foundations of Categorical Model Theory, Contemp. Math. 104, Amer. Math. Soc., 1989.
  • [MPi] M. Makkai and A. M. Pitts, Some results on locally finitely presentable categories, Trans. Amer. Math. Soc. 299 (1987), 473-495.
  • [MR] M. Makkai and G. E. Reyes, First Order Categorical Logic, Lecture Notes in Math. 611, Springer, Berlin, 1977.
  • [AP] A. M. Pitts, An application of open maps to categorical logic, J. Pure Appl. Algebra 29 (1983), 313-326.
  • [V] H. Vogler, Preservation theorems for limits of structures and global sections of sheaves of structures, Math. Z. 166 (1979), 27-53.
  • [MZ] M. W. Zawadowski, Descent and duality, Ann. Pure Appl. Logic, 71 (1995), 131-185.
  • [MZ1] M. W. Zawadowski, Un théorème de la descente pour les prétopos, Thèse de doctorat, Université de Montréal, 1989.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: Primary 03G30, 18C10; Secondary 03C40, 18D05.
Identyfikator YADDA
bwmeta1.element.zamlynska-6bb9d2b7-234c-4e9f-8a17-24ecbae7658a
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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