1 citations · 2 across the 9 of their papers we have counts for
10 papers
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…
Morse-Bott inequalities for endomorphisms
Enrique Macías-Virgós, Alejandro O. Majadas-Moure, David Mosquera-Lois +1
Let be a finite simplicial complex, let be a simplicial map and let be a discrete Morse-Bott function on satisfying for all simplice…
A Computational (Co)homological Approach to Contiguity Distance
Enrique Macías-Virgós, Ángel Méndez-Vázquez, David Mosquera-Lois
We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refi…
Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
Enrique Macías-Virgós, Daniel Tanré
Let be the quasi-projective subspace of the symplectic group . In this short note, we prove that the subspace Lusternik-Schnirelmann category of in $\ma…
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…
Lefschetz fixed-object and fixed-morphism theorems for acyclic categories
Samuel Castelo-Mourelle, Enrique Macías-Virgós, David Mosquera-Lois
We introduce two novel complementary notions of the Lefschetz number for a functor from a finite acyclic category to itself and we prove a Lefschetz fixed-object theorem and a Lefs…
Relative De Rham cohomology in diffeological spaces
Enrique Macías-Virgós, Reihaneh Mehrabi
We define two different versions of the relative De Rham cohomology groups of a diffeological space. Additionally, we study a variant of the Mayer-Vietoris sequence and discuss the…
Mayer-Vietoris sequence for generating families in diffeological spaces
Enrique Macías-Virgós, Reihaneh Mehrabi
We prove a version of the Mayer-Vietoris sequence for De Rham differential forms in diffeological spaces. It is based on the notion of a generating family instead of that of a cove…
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…
Ganea and Whitehead definitions for the tangential Lusternik-Schnirelmann category of foliations
Jean-Paul Doeraene, Enrique Macias-Virgós, Daniel Tanré
This work solves the problem of elaborating Ganea and Whitehead definitions for the tangential category of a foliated manifold. We develop these two notions in the category $\Tops$…