4 papers · 1 filter
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…
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…