# Span and cospan representations of weak double categories

Document Type: Research Paper

Authors

1 Dipartimento di Matematica, Universita 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

### References

[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.