Span and cospan representations of weak double categories | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 9، دوره 6، Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)، فروردین 2017، صفحه 85-105 اصل مقاله (489.6 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Marco Grandis1؛ Robert Par\'e2 | ||
| 1Dipartimento di Matematica, Universit\`a di Genova, Via Dodecaneso 35, 16146-Genova, Italy | ||
| 2Department of Mathematics and Statistics, Dalhousie University, Halifax NS, Canada B3H 4R2 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Double category؛ tabulator؛ span | ||
| مراجع | ||
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[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. | ||
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