Standard

Categories Without Structures. / Rodin, A. .

In: Philosophia Mathematica, Vol. 19, No. 1, 2011, p. 20-46.

Research output: Contribution to journal › Article › peer-review

Harvard

Rodin, A 2011, 'Categories Without Structures', Philosophia Mathematica, vol. 19, no. 1, pp. 20-46. https://doi.org/DOI: 10.1093/philmat/nkq027

APA

Rodin, A. (2011). Categories Without Structures. Philosophia Mathematica, 19(1), 20-46. https://doi.org/DOI: 10.1093/philmat/nkq027

Vancouver

Rodin A. Categories Without Structures. Philosophia Mathematica. 2011;19(1):20-46. https://doi.org/DOI: 10.1093/philmat/nkq027

Author

Rodin, A. . / Categories Without Structures. In: Philosophia Mathematica. 2011 ; Vol. 19, No. 1. pp. 20-46.

BibTeX

@article{654bce4e3e5242c2a78d88633bedc7c0,
title = "Categories Without Structures",
abstract = "The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies “invariant forms” (Awodey) categorical mathematics studies covariant transformations which, generally, don{\textquoteright}t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.",
keywords = "Category theory, Structuralism, Invariance, Functoriality",
author = "A. Rodin",
year = "2011",
doi = "DOI: 10.1093/philmat/nkq027",
language = "English",
volume = "19",
pages = "20--46",
journal = "Philosophia Mathematica",
issn = "0031-8019",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Categories Without Structures

AU - Rodin, A.

PY - 2011

Y1 - 2011

N2 - The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies “invariant forms” (Awodey) categorical mathematics studies covariant transformations which, generally, don’t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.

AB - The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies “invariant forms” (Awodey) categorical mathematics studies covariant transformations which, generally, don’t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.

KW - Category theory

KW - Structuralism

KW - Invariance

KW - Functoriality

U2 - DOI: 10.1093/philmat/nkq027

DO - DOI: 10.1093/philmat/nkq027

M3 - Article

VL - 19

SP - 20

EP - 46

JO - Philosophia Mathematica

JF - Philosophia Mathematica

SN - 0031-8019

IS - 1

ER -

ID: 5406416