A theory of 2-Pro-objects

• Autores: Descotte, María Emilia; Dubuc, Eduardo Julio
• Año de publicación: 2014
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: 2-PRO-OBJECT; 2-FILTERED; PSEUDO-LIMIT
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In [1], Grothendieck develops the theory of pro-objects over a category C . The fundamental property of the category Pro(C) is that there is an embedding C c −→ Pro(C), the category Pro(C) is closed under small cofiltered limits, and these limits are free in the sense that for any category E closed under small cofiltered limits, pre-composition with c determines an equivalence of categories Cat(Pro(C), E)+ 'Cat(C, E), (where the ” + ” indicates the full subcategory of the functors preserving cofiltered limits). In this paper we develop a 2-dimensional theory of pro-objects. Given a 2-category C , we define the 2-category 2-Pro(C) whose objects we call 2-pro-objects. We prove that 2-Pro(C) has all the expected basic properties adequately relativized to the 2-categorical setting, including the universal property corresponding to the one described above. We have at hand the results of Cat -enriched category theory, but our theory goes beyond the Cat -enriched case since we consider the non strict notion of pseudo-limit, which is usually that of practical interest.
Fil: Descotte, María Emilia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dubuc, Eduardo Julio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina