Categories of Functional Analysis

• Autores: Chávez Guevara, Leonaldo, Rivero Zapata, Alberto Mariano
• Formato: artículo
• Fecha de Publicación: 2024
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:revistasinvestigacion.unmsm.edu.pe:article/27235
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/27235
• Nivel de acceso: acceso abierto
• Materia: Category; Funtor; Banach Algebra; Gelfand Theory; Categoría; Algebra de Banach; Teoria de Gelfand

The objective of this article is to categorically focus on some aspects of Functional Analysis, aiming to present a high-level methodology for research and teaching. In section 1 the notions of category and subcategory are given; The Identification Convention and the Principle of Duality are stated; Some categories are presented and important properties of their objects and morphisms are stated. In section 2, functors and natural transformations are studied, showing their importance through examples that connect algebra and topology. In section 3 the important notions of limit of a functor and of adjunction of functors are given, and some examples are considered.