Generalized Homotopy in C-Categories
Generalized Homotopy in C-Categories
A \(C\)-category is a category with a class of fibrations and a cone endofunctor \(C\) subject to suitable axioms. The authors define homotopy groups associated to pairs of morphisms of the form \(i: B\to A\), \(h: CA\to X\) in a \(C\)-category, where \(i\) is a cofibration. They interpret these homotopy groups as the homotopy groups of Kan complexes, and they construct exact sequences. The theory is is an axiomatization of homotopy groups relative to bases more general than base points, for example base rays.
Función del cono, 12 Matemáticas, category with a natural cone, Simplicial sets; simplicial objects in a category, 1202.25 Espacios Lineales Topológicos, Abstract and axiomatic homotopy theory in algebraic topology, Estructura de homotopía, 530, Homotopy Theory, 510, C-category, Cone functor, pointed homotopy theory, Homotopy structure, Teoría de la homotopía
Función del cono, 12 Matemáticas, category with a natural cone, Simplicial sets; simplicial objects in a category, 1202.25 Espacios Lineales Topológicos, Abstract and axiomatic homotopy theory in algebraic topology, Estructura de homotopía, 530, Homotopy Theory, 510, C-category, Cone functor, pointed homotopy theory, Homotopy structure, Teoría de la homotopía
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