Structures in Concrete Categories
Henri Bourl\`es
TL;DR
This paper defines structures in concrete categories to connect Bourbaki's set-based approach with the categorical language, enhancing the understanding of mathematical structures.
Contribution
It introduces a formal definition of structures within concrete categories, bridging the gap between Bourbaki's structural approach and category theory.
Findings
Provides an explicit definition of structures in concrete categories
Bridges the conceptual gap between set-based and categorical frameworks
Facilitates the application of category theory to classical structural mathematics
Abstract
The monumental treatise "\'El\'ements de math\'ematique" of N. Bourbaki is based on the notion of structure and on the theory of sets. On the other hand, the theory of categories is based on the notions of morphism and functor. An appropriate definition of a structure in a concrete category is given in this paper. This definition makes it possible to bridge the gap between Bourbaki's structural approach and the categorical language.
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Taxonomy
TopicsOptics and Image Analysis · Constraint Satisfaction and Optimization