Open AccessCategorical definitions and properties via generators
Author(s) -
Gustavo Arengas
Publication year - 2019
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v53n2.85525
Subject(s) - functor , categorical variable , mathematics , iterated function , algebra over a field , pure mathematics , category theory , adjoint functors , mathematical analysis , statistics
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.