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Categorical set theory

Last updated March 01, 2026

Categorical set theory is any one of several versions of set theory developed from or treated in the context of mathematical category theory. Its basis originated with the development of ETCS by William Lawvere in 1964.^[1]

References

Inline

↑ Osius, Gerhard (February 1974). "Categorical set theory: A characterization of the category of sets". Journal of Pure and Applied Algebra. 4 (1): 79–119. doi:10.1016/0022-4049(74)90032-2.

General

Barr, M.; Wells, C. (1996). Category Theory for Computing Science (2nd ed.). Prentice Hall. ISBN 978-0-13-323809-9.
Bourbaki, N. (1994). Elements of the History of Mathematics. Translated by Meldrum, John. Springer. doi:10.1007/978-3-642-61693-8. ISBN 978-3-642-61693-8.
Kelley, J.L. (2017) [1955]. General Topology. Dover. ISBN 978-0-486-81544-2.
Lambek, J.; Scott, P.J. (1988). Introduction to Higher Order Categorical Logic. Cambridge studies in advanced mathematics. Vol. 7. Cambridge University Press. ISBN 978-0-521-35653-4.
Lawvere, F.W.; Rosebrugh, R. (2003). Sets for Mathematics. Cambridge University Press. ISBN 978-0-521-01060-3.
Lawvere, F.W.; Schanuel, S.H. (2009). Conceptual Mathematics: A First Introduction to Categories (2nd ed.). Cambridge University Press. ISBN 978-1-139-64396-2.
Kiyosi Itô, ed. (2000) [1993]. Encyclopedic Dictionary of Mathematics (2nd ed.). MIT Press. ISBN 0-262-59020-4.
Mitchell, J.C. (1996). Foundations for Programming Languages. MIT Press. ISBN 978-0-585-03789-9. OCLC 48138995.
Nestruev, J. (2003). Smooth Manifolds and Observables. Springer. ISBN 0-387-95543-7.
Poizat, B. (2012) [2000]. A Course in Model Theory: An Introduction to Contemporary Mathematical Logic. Translated by Klein, Moses. Springer. ISBN 978-1-4419-8622-1.

External links

Leinster, Tom (2014). "Rethinking set theory". American Mathematical Monthly. 121 (5): 403–415. arXiv: 1212.6543 . CiteSeerX 10.1.1.751.6210 . doi:10.4169/amer.math.monthly.121.05.403. S2CID 5732995.

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[1] Osius, Gerhard (February 1974). "Categorical set theory: A characterization of the category of sets". Journal of Pure and Applied Algebra. 4 (1): 79–119. doi:10.1016/0022-4049(74)90032-2.

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