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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá July/Dec. 2019 Epub Mar 20, 2020
Artículos originales
Categorical definitions and properties via generators
Definiciones y propiedades categóricas vía generadores
1Universidad Nacional de Colombia, Bogotá, Colombia, Departamento de matemáticas, Facultad de ciencias carrera 30, calle 45, e-mail: gearengasr@unal.edu.co
In the present work, we show how the study of categorical constructions does not have to be done with all the objects of the category, but we can restrict ourselves to work with families of generators. Thus, universal properties can be characterized through iterated families of generators, which leads us in particular to an alternative version of the adjoint functor theorem. Similarly, the properties of relations or subobjects algebra can be investigated by this method. We end with a result that relates various forms of compactness through representable functors of generators.
Key words and phrases. Generators; universal property; adjoint functor theorem; relations; subobjects algebra; compactness
En el presente trabajo mostramos como el estudio de las construcciones categóricas no tiene porque realizarse con todos los objetos de la categoría, sino que podemos restringirnos a trabajar con familias de generadores. Así, las propiedades universales pueden ser caracterizadas a traves de familias iteradas de generadores, lo que nos lleva en particular a una versión alternativa del teorema del funtor adjunto. De igual forma, las propiedades de las relaciones o del álgebra de subobjetos pueden ser investigadas por este método. Terminamos con un resultado que relaciona diversas formas de compacidad a través de funtores representables de generadores.
Palabras y frases clave. Generadores; propiedad universal; teorema funtor adjunto; relaciones; álgebra de subobjetos; compacidad
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Received: October 2018; Accepted: August 2019