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Fundamenta Mathematicae

1999 | 160 | 3 | 269-286
Tytuł artykułu

Bimorphisms in pro-homotopy and proper homotopy

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. The category is balanced if every bimorphism is an isomorphism. In the paper properties of bimorphisms of several categories are discussed (pro-homotopy, shape, proper homotopy) and the question of those categories being balanced is raised. Our most interesting result is that a bimorphism f:X → Y of $tow(H_0)$ is an isomorphism if Y is movable. Recall that $\tow(H_0)$ is the full subcategory of $pro-H_0$ consisting of inverse sequences in $H_0$, the homotopy category of pointed connected CW complexes.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
269-286
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-09-29
poprawiono
1999-01-18
Twórcy
autor
• Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A., dydak@math.utk.edu
Bibliografia
• [B] H. J. Baues, Foundations of proper homotopy theory, Draft manuscript, Max-Planck-Institut für Math., 1992.
• [Br] E. M. Brown, Proper homotopy theory in simplicial complexes, in: Topology Conference (Virginia Polytechnic Institute and State University), R. F. Dickmann Jr. and P. Fletcher (eds.), Lecture Notes in Math. 375, Springer, Berlin, 1974, 41-46.
• [C-G] C. Casacuberta and S. Ghorbal, On homotopy epimorphisms of connective covers, preprint, 1997.
• [D1] J. Dydak, The Whitehead and the Smale theorems in shape theory, Dissertationes Math. 156 (1979).
• [D2] J. Dydak, Epimorphism and monomorphism in homotopy, Proc. Amer. Math. Soc. 116 (1992), 1171-1173.
• [D-S1] J. Dydak and J. Segal, Shape Theory: An Introduction, Lecture Notes in Math. 688, Springer, Berlin, 1978.
• [D-S2] J. Dydak and J. Segal, Strong shape theory, Dissertationes Math. 192 (1981).
• [Dy-R] E. Dyer and J. Roitberg, Homotopy-epimorphism, homotopy-monomorphism and homotopy-equivalences, Topology Appl. 46 (1992), 119-124.
• [Ed-H] D. A. Edwards and H. M. Hastings, Čech and Steenrod Homotopy Theories with Applications to Geometric Topology, Lecture Notes in Math. 542, Springer, Berlin, 1976.
• [En1] R. Engelking, General Topology, Heldermann, Berlin, 1989.
• [F-T-W] F. T. Farrell, L. R. Taylor and J. B. Wagoner, The Whitehead theorem in the proper category, Compositio Math. 27 (1973), 1-23.
• [G] S. Ghorbal, Epimorphisms and monomorphisms in homotopy theory, PhD Thesis, Université Catholique de Louvain, 1996 (in French).
• [H-R] P. Hilton and J. Roitberg, Relative epimorphisms and monomorphisms in homotopy theory, Compositio Math. 61 (1987), 353-367.
• [H-W] L. Hong and S. Wenhuai, Homotopy epimorphisms in homotopy pushbacks, Topology Appl. 59 (1994), 159-162.
• [M-S] S. Mardešić and J. Segal, Shape Theory, North-Holland, Amsterdam, 1982.
• [Mat] M. Mather, Homotopy monomorphisms and homotopy pushouts, Topology Appl. 81 (1997), 159-162.
• [Mo-P] M. A. Morón and F. R. Ruiz del Portal, On weak shape equivalences, ibid. 92 (1999), 225-236.
• [Mu] G. Mukherjee, Equivariant homotopy epimorphisms, homotopy monomorphisms and homotopy equivalences, Bull. Belg. Math. Soc. 2 (1995), 447-461.
• [P] T. Porter, Proper homotopy theory, in: Handbook of Algebraic Topology, Elsevier Science, 1995, 127-167.
• [S] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
• [Sp] S. Spież, A majorant for the family of all movable shapes, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 615-620.
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Bibliografia
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