General associativity and general composition for double categories

Robert Dawson; Robert Pare

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1993)

  • Volume: 34, Issue: 1, page 57-79
  • ISSN: 1245-530X

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Dawson, Robert, and Pare, Robert. "General associativity and general composition for double categories." Cahiers de Topologie et Géométrie Différentielle Catégoriques 34.1 (1993): 57-79. <http://eudml.org/doc/91515>.

@article{Dawson1993,
author = {Dawson, Robert, Pare, Robert},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {horizontal composition; vertical composition; square; pinwheel; double category; iterated mixed composition},
language = {eng},
number = {1},
pages = {57-79},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {General associativity and general composition for double categories},
url = {http://eudml.org/doc/91515},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Dawson, Robert
AU - Pare, Robert
TI - General associativity and general composition for double categories
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1993
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 34
IS - 1
SP - 57
EP - 79
LA - eng
KW - horizontal composition; vertical composition; square; pinwheel; double category; iterated mixed composition
UR - http://eudml.org/doc/91515
ER -

References

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  1. 1 A. Bastiani and C. Ehresmann, Multiple Functors I. Limits Relative to Double Categories, Cahiers de Top. et Géom. Diff.XV-3 (1974), pp. 215-291. Zbl0332.18005MR379626
  2. 2 R. Brown and C.B. Spencer, Double groupoids and crossed modules, Cahiers Top. et Géom. Diff.XVII-4 (1976), pp. 343-362. Zbl0344.18004MR440553
  3. 3 R. Dawson and R. Paré, Characterizing Tileorders, to appear. Zbl0790.05020MR1253709
  4. 4 R. Dawson and R. Paré, Canonical Factorizations in Double Categories, in preparation. Zbl0778.18005
  5. 5 C. Ehresmann, Catégories Structurées, Ann. Sci. Ecole Norm. Sup.80 (1963), pp. 349-425. Zbl0128.02002MR197529
  6. 6 C. Ehresmann, Catégories et Structures, Dunod, Paris, 1965. Zbl0192.09803MR213410
  7. 7 A. and C. Ehresmann, Multiple Functors IV. Monoidal Closed Structures on Catn, Cahiers de Top. et Géom. Diff.XX-1, pp. 59-104. Zbl0415.18007
  8. 8 J.W. Gray, Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Math, 391, Springer1974. Zbl0285.18006MR371990
  9. 9 M. Johnson, Pasting Diagrams in n-Categories with Applications to Coherence Theorems and Categories of Paths, Ph.D. thesis, University of Sydney, 1987. 
  10. 10 G.M. Kelly and R. Street, Review of the Elements of 2-Categories, in Category Seminar, Lecture Notes in Math.420, pp, 75-103. Zbl0334.18016MR357542
  11. 11 R. Paré, Double Limits, in preparation. Zbl0939.18007
  12. 12 A.J. Power, A 2-Categorial Pasting Theorem, J. of Algebra, 1990, 129 (2) pp. 439-445. Zbl0698.18005MR1040947
  13. 13 P.H. Palmquist, The Double Category of Adjoint Squares, Lecture Notes in Math.195, pp. 123-153. Zbl0263.18004MR289600
  14. 14 C.B. Spencer, An abstract setting for homotopy pushouts and pullbacks, Cahiers de Top. et Géom. Diff.XVIII (1977), pp. 409-429. Zbl0378.18008MR486054
  15. 15 C.B. Spencer and Y.L. Wong, Pullback and pushout squares in a special double category with connection, Cahiers de Top. et Géom. Diff.XXIV (1983), pp. 161-192. Zbl0519.18008MR710039

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