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Categorical set theory

{{Short description|Sets defined using mathematical category theory}}

Categorical set theory is any one of several versions of set theory developed from or treated in the context of mathematical category theory.

See also

References

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  • {{cite book |author1-link=Michael Barr (mathematician) |author2-link=Charles Wells (mathematician) |last1=Barr |first1=M. |last2=Wells |first2=C. |title=Category Theory for Computing Science |publisher=Prentice Hall |edition=2nd |date=1996 |isbn=978-0-13-323809-9 }}
  • {{cite book |author-link=Nicolas Bourbaki |first=N. |last=Bourbaki |translator-first=John |translator-last=Meldrum|translator-link=John D. P. Meldrum |title=Elements of the History of Mathematics |year=1994 |publisher=Springer |isbn=978-3-642-61693-8 |doi=10.1007/978-3-642-61693-8 |url={{GBurl|4JprCQAAQBAJ|pg=PP7}}}}
  • {{cite book |author-link=John L. Kelley |first=J.L. |last=Kelley |title=General Topology |publisher=Dover |orig-date=1955 |date=2017 |isbn=978-0-486-81544-2 |url={{GBurl|DfbODQAAQBAJ|pg=PR8}}}}
  • {{cite book |author1-link=Joachim Lambek |author2-link=P.J. Scott |last1=Lambek |first1=J. |last2=Scott |first2=P.J. |title=Introduction to Higher Order Categorical Logic |publisher=Cambridge University Press |series=Cambridge studies in advanced mathematics |volume=7 |date=1988 |isbn=978-0-521-35653-4 |url={{GBurl|6PY_emBeGjUC|pg=PR5}}}}
  • {{cite book |author1-link=Francis William Lawvere |author2-link=Robert Rosebrugh |last1=Lawvere |first1=F.W. |last2=Rosebrugh |first2=R. |title=Sets for Mathematics |publisher=Cambridge University Press |date=2003 |isbn=978-0-521-01060-3 |url={{GBurl|h3_7aZz9ZMoC|pg=PP1}}}}
  • {{cite book |last1=Lawvere |first1=F.W. |author2-link=Stephen H. Schanuel |last2=Schanuel |first2=S.H. |title=Conceptual Mathematics: A First Introduction to Categories |publisher=Cambridge University Press |edition=2nd |date=2009 |isbn=978-1-139-64396-2 |url={{GBurl|6G0gAwAAQBAJ|pg=PR7}}}}
  • {{cite book |author-link=Mathematical Society of Japan |author= |title=Encyclopedic Dictionary of Mathematics |edition=2nd |editor=Kiyosi Itô |publisher=MIT Press |orig-year=1993 |isbn=0-262-59020-4 |date=2000 |url={{GBurl|WHjO9K6xEm4C|pg=PR5}}}}
  • {{cite book |author-link=John C. Mitchell |first=J.C. |last=Mitchell |title=Foundations for Programming Languages |publisher=MIT Press |date=1996 |isbn=978-0-585-03789-9 |oclc=48138995 |url=https://archive.org/details/foundationsforpr0000mitc}}
  • {{cite book |author-link=Jet Nestruev |first=J. |last=Nestruev |title=Smooth Manifolds and Observables |publisher=Springer |date=2003 |isbn=0-387-95543-7 |url={{GBurl|vTrhBwAAQBAJ|pg=PR12}}}}
  • {{cite book |author-link=Bruno Poizat |translator-first=Moses |translator-last=Klein |first=B. |last=Poizat |title=A Course in Model Theory: An Introduction to Contemporary Mathematical Logic |publisher=Springer |date=2012 |orig-date=2000 |isbn=978-1-4419-8622-1 |url={{GBurl|_WXgBwAAQBAJ|pg=PR16}}}}

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External links

  • {{cite journal |first=Tom |last=Leinster |title=Rethinking set theory |journal=American Mathematical Monthly |volume=121 |issue=5 |pages=403–415 |date=2014 |doi=10.4169/amer.math.monthly.121.05.403 |citeseerx=10.1.1.751.6210 |arxiv=1212.6543|s2cid=5732995 }}

Category:Category theory

Category:Set theory

Category:Formal methods

Category:Categorical logic

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