Categories as mathematical models

@article{Spivak2018CategoriesAM,
  title={Categories as mathematical models},
  author={David I. Spivak},
  journal={arXiv: Category Theory},
  year={2018}
}
  • David I. Spivak
  • Published 22 September 2014
  • Mathematics
  • arXiv: Category Theory
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical… 
View PDF on arXiv
4 Citations
Background Citations
1

4 Citations

Are There Category-Theoretical Explanations of Physical Phenomena?

The problem of mathematical explanations in science has been discussed extensively in the philosophical literature in recent years. This paper is devoted to the question of whether category theory…

MAPPING AND ENHANCING DESIGN STUDIES WITH PSI META-THEORETIC DESIGN FRAMEWORK

TLDR
This paper proposes a model-based approach that on the one hand, does not delve into the details of the design object itself, but on the other hand, unifies the description of design problem at another abstraction level and allows for describing and comparing underlying models of published design studies using the same language.

Modeling the Internet of Things: A Foundational Approach

TLDR
It is argued that category theory, a branch of abstract mathematics, provides a firm conceptual foundation for information modeling which already meets most of these criteria and is suitable for application in applied contexts.

Transforming Health Care through Digital Revolutions

TLDR
The P9 health care concept is introduced, followed by a discussion of a framework for smart health care, and examples of ongoing work at the National Institute of Standards and Technology (NIST) are presented.