Given a bicategory C and a family W of arrows of C, we give conditions on the pair (C, W) that allow us to construct the bicategorical localization with respect to W by dealing only with the 2-cells, that is without adding ...

Esta dissertação é uma humilde introdução a grandes ferramentas da teoria da homotopia abstrata: categorias modelo e ∞-categorias (através de quasicategorias). A primeira parte do texto apresenta estas estruturas, conectando ...

We relate the Davis-Lück homology with coefficients in Weibel's homotopy K-theory to the equivariant algebraic kk-theory using homotopy theory and adjointness theorems. We express the left hand side of the assembly map for ...

§  Simplicial Systems. Definition. (1) A simplicial system over  a category C is a triple [Formula Matemática]

The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a ...

The concept of model category is due to Quillen [1]. It represents an axiomatic aproach to homotopy in which not only homotopy itself but also several of the concepts of Algebraic Topology are developed, such as fibrations, ...

The objective of this work is to generalize basic ideas from linear algebra and topology, such as traces and fixed points, into a categorical context. Each of those generalizations has important objects and ideas behind, ...