Results 171 to 180 of about 17,688 (209)

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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Category Theory in Physics, Mathematics, and Philosophy

Springer Proceedings in Physics, 2019
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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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Mathematical theory on formation of category detecting nerve cells

Biological Cybernetics, 1978
The nerve cells are believed to have such ability of self-organization that, given a number of input patterns, each cell tunes itself to become responsive to only one of the patterns, or to one subset of patterns having some features in common. The detectors of patterns or pattern subsets are formed in this manner.
Amari, Shun-ichi, Takeuchi, Akikazu
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Category Theory: The Language of Mathematics

Philosophy of Science, 1999
In this paper I argue that category theory ought to be seen as providing thelanguagefor mathematical discourse. Against foundational approaches, I argue that there is no need toreduceeither the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories.
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Mathematical Applications of Category Theory

1984
The interaction between category theory and set theory by A. Blass Synthetic calculus of variations by M. Bunge and M. Heggie The representation of limits, lax limits and homotopy limits as sections by J. W. Gray Open locales and exponentiation by P. T. Johnstone Eilenberg-Mac Lane toposes and cohomology by A. Joyal and G. Wraith A combinatorial theory
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Semantic Category theory and Semantic Intertwine: the anathema of mathematics

Kybernetes, 2014
Purpose – The recent scientific observation that human information processing involves four independent data types, has pinpointed a source of fallacious arguments within many domains of human thought. The species-unique ability to assign observable characteristics to purely conceptual entities has created beautiful ...
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