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A general theory of polyhedral sets and the corresponding T-complexes

Seria
Rozprawy Matematyczne tom/nr w serii: 266 wydano: 1988
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Warianty tytułu
Abstrakty
EN

CONTENTS
Preface......................................................................................................5
Introduction...............................................................................................6
1. A class of model categories.................................................................10
1.1 Categories with models......................................................................10
1.2. Cone-complexes...............................................................................12
1.3. Three standard constructions..........................................................14
1.4. Marked cone-complexes and the category Poly...............................16
1.5. Consequences of the marked face structure of a polycell................19
1.6. Subcategories of Poly appropriate as model categories..................23
2. Posets and shellability.........................................................................26
2.1. Shelling............................................................................................26
2.2. The class ET of model categories....................................................29
2.3. Face posets of S-polycells...............................................................32
2.4. The equivalence SPoly → SPos.......................................................36
3. Equivalences of categories of T-complexes.........................................40
3.1. T-complexes.....................................................................................40
3.2. The isomorphism ∆TC → ∆₁TC........................................................42
3.3. Structures and collapsing.................................................................45
3.4. Particular collapses in Sd X and VX..................................................47
3.5. The collapse $A(∆^n)$ in Sd $∆^n - p ∆^n$.......................................55
3.6. The functor $e_ℳ$, from ∆₁T-complexes to ℳ T-complexes...........62
3.7. The natural equivalence $r_ℳ ∘ e_ℳ ≃1$.....................................63
3.8. The equivalence of categories.........................................................65
4. Degeneracy structures in ℳ T-complexes...........................................67
4.1. An approach to degeneracy structures in ℳ T-complexes...............68
4.2. Pseudocylinder structures on SC-complexes...................................70
4.3. Rectifiers on pseudocylinders..........................................................74
4.4. Degenerate elements in an ℳ T-complex........................................77
4.5. Functors between categories of T-complexes..................................83
4.6. Suggested proof of Claims 5.4 and 5.10..........................................86
5. Comments and possibilities for further work........................................92
Appendix. S-shellability of cone-complexes.............................................98
Glossary of symbols..............................................................................106
References...........................................................................................109
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 266
Liczba stron
111
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXVI
Daty
wydano
1988
Twórcy
  • Department of Pure Mathematics, University College of North Wales, Bangor, Gwynedd L57 2UW, United Kingdom
Bibliografia
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Języki publikacji
EN
Uwagi
Errata Page, line: 5⁴ For: Asley, 1988 Read: Ashley, 1988
Identyfikator YADDA
bwmeta1.element.zamlynska-5249ebed-3daf-4fca-866d-334e4e45afee
Identyfikatory
ISBN
83-01-08117-1
ISSN
0012-3862
Kolekcja
DML-PL
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