论文信息 - DOUBLE CATEGORIES, 2-CATEGORIES, THIN STRUCTURES AND CONNECTIONS

DOUBLE CATEGORIES, 2-CATEGORIES, THIN STRUCTURES AND CONNECTIONS

The main result is that two possible structures which may be imposed on an edge symmetric double category, namely a connection pair and a thin structure, are equivalent. A full proof is also given of the theorem of Spencer, that the category of small 2-categories is equivalent to the category of edge symmetric double categories with thin structure.

Ronald T. Brown | Ghafar H. Mosa | Robert Pare

[1] P. J. Higgins,et al. ON THE CONNECTION BETWEEN THE SECOND RELATIVE HOMOTOPY GROUPS OF SOME RELATED SPACES , 1978 .

[2] R. Brown,et al. Low-Dimensional Topology: Higher-dimensional group theory , 1982 .

[3] P. J. Higgins,et al. On the algebra of cubes , 1981 .

[4] R. Steiner,et al. Nerves of Multiple Categories , 1993 .

[5] Charles Ehresmann,et al. Multiple functors. IV. Monoidal closed structures on $Cat_n$ , 1979 .

[6] An abstract setting for homotopy pushouts and pullbacks , 1977 .

[7] P. J. Higgins,et al. The equivalence of $\infty$-groupoids and crossed complexes , 1981 .

[8] Robert J. MacG. Dawson,et al. General associativity and general composition for double categories , 1993 .

[9] Ronald Brown,et al. Double groupoids and crossed modules , 1976 .

[10] Charles Ehresmann,et al. Catégories structurées III. Quintettes et applications covariantes , 1963 .

[11] P. J. Higgins,et al. Tensor products and homotopies for ω-groupoids and crossed complexes , 1987 .