7 papers
Motion planning and topological complexity for diagrams of spaces
Isaac Carcacía-Campos
A diagram of spaces describes a system of interacting state spaces. Motion planning in such a system is not merely an objectwise problem since the selected paths must form a natura…
Vector fields, initial scaffolds and database reduction
Isaac Carcacía-Campos
Reduction replaces a mathematical object with a simpler model that retains the relevant information. We introduce left and right vector fields on small categories as tools for redu…
Reducing and Classifying Fiber Bundles over Small Categories
Isaac Carcacía-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…
Subword representations and weak hypercube dimension for acyclic categories
Isaac Carcacía-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…
Weak and Strong Fibrations of Functors
Isaac Carcacía-Campos, Enrique Macías-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 Carcacía-Campos, Enrique Macías-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…
Homotopy invariants in small categories
I. Carcacía-Campos, E. Macías-Virgós, D. Mosquera-Lois
Tanaka introduced a notion of Lusternik Schnirelmann category, denoted , of a small category . Among other properties, he proved an analog…