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Category Theory in Physics, Mathematics, and Philosophy

Springer Proceedings in Physics, 2019
The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to
Skowron, Bartłomiej, Kuś, Marek
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Category theory and the foundations of mathematics: Philosophical excavations

SynthÈse, 1995
The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the ...
Jean-Pierre Marquis
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Mathematical Modelling by Help of Category Theory

Mathematical Engineering
Die Lösung eines jeden ingenieurtechnischen Problems beginnt mit einem Modellierungsprozess, der ein Modell bereitstellt, das ein zu betrachtendes System darstellt. Die entscheidende Frage für die praktische Verwendung von Modellen besteht darin, zu beurteilen, ob das Modell und die Ergebnisse seiner Verwendung vertrauenswürdig sind.
Dmitrii Legatiuk
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Category Theory as a Mathematics for Formalizing Ontologies

2010
Category theory is discussed as an appropriate mathematical basis for the formalization and study of ontologies. It is based upon the notion of the structure manifest in systems of compositional relations and through mappings between systems that preserve composition.
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Category Theory and Structuralism in Mathematics: Syntactical Considerations

1997
Thus, to be is to be related and the “essence” of an “entity” is given by its relations to its “environment”. This claim is striking: it seems to describe perfectly well the way objects of a category are characterized and studied. Consider, for instance, the fundamental notion of product in a category C: a product for two objects A and B of C is an ...
Jean-Pierre Marquis
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Husserl, Intentionality and Mathematics: Geometry and Category Theory

2022
Romero Contreras Arturo
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MATHEMATICS: FROM SET THEORY TO CATEGORY THEORY

Metaphysics, 2022
The basis of mathematics is set theory, to which almost all mathematical directions go back. However, the importance of category theory for mathematics as a whole is steadily increasing. If in set theory the determining role is played by the internal structure of the object under consideration, then in category theory an object is characterized by its ...
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Rethinking equality in mathematics education with category theory

The Mathematics Enthusiast
Kelly Paton
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