5 papers
Directed Homotopy, Sectional Invariants, and Functorial Databases
Isaac CarcacÃa-Campos
A database instance on a small category may be represented as a set-valued functor or, equivalently, as a discrete opfibration. Its sections correspond to globally coherent choices…
Subword representations and weak hypercube dimension for acyclic categories
Isaac CarcacÃa-Campos
We introduce a categorical analogue of weak hypercube representations of finite posets by means of faithful embeddings into categories of subwords of finite words. For finite acycl…
Reducing and Classifying Fiber Bundles over Small Categories
Isaac CarcacÃa-Campos
A fiber bundle over a small category is a locally constant family of categories whose transition functors encode how a fixed fiber is transported over the base. Its Grothendieck co…
Weak and Strong Fibrations of Functors
Isaac CarcacÃa-Campos, Enrique MacÃas-Virgós, David Mosquera-Lois
We develop a homotopical framework for small categories that extends classical invarints of algebraic topology to the categorical setting. Our approach is based on the construction…
Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Isaac CarcacÃa-Campos, Enrique MacÃas-Virgós, David Mosquera-Lois
We prove that for a bifibration P between small categories, the lenght of the cup product in the kernel of the induced morphism in the Baues-Wirsching cohomology with coefficients…