Span and cospan representations of weak double categories

Document Type: Research Paper

Authors

1 Dipartimento di Matematica, Universit`a di Genova, Via Dodecaneso 35, 16146-Genova, Italy

2 Department of Mathematics and Statistics, Dalhousie University, Halifax NS, Canada B3H 4R2

Abstract

We prove that many important weak double categories can be `represented' by spans, using the basic higher limit of the theory: the tabulator. Dually, representations by cospans via cotabulators are also frequent.

Keywords


[1] Benabou, J., Introduction to Bicategories", in: Reports of the Midwest Category Seminar, Lecture Notes in Math. 47, Springer, Berlin 1967, 1-77.
[2] Ehresmann, C., Categories structurees, Ann. Sci. Ec. Norm. Super. 80 (1963), 349-425.
[3] Ehresmann, C., Categories et structures", Dunod, Paris, 1965.
[4] Grandis, M. and R. Pare, Limits in double categories, Cah. Topol. Geom. Differ. Categ. 40 (1999), 162-220.
[5] Grandis, M. and R. Pare, Adjoint for double categories, Cah. Topol. Geom. Differ. Categ. 45 (2004), 193-240.
[6] Grandis, M. and R. Pare, Kan extensions in double categories (On weak double categories, III), Theory Appl. Categ. 20(8) (2008), 152-185.
[7] Grandis, M. and R. Pare, Lax Kan extensions for double categories (On weak double categories, Part IV), Cah. Topol. Geom. Differ. Categ. 48 (2007), 163-199.
[8] Niefeld S., Span, cospan, and other double categories, Theory Appl. Categ. 26(26) (2012), 729-742.
[9] Street, R., Limits indexed by category-valued 2-functors, J. Pure Appl. Alg. 8 (1976), 149-181.