Pataraia's theorem
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In mathematics, Pataraia's theorem states each monotone map for an inductive poset admits a least fixed point, where an inductive poset means a dcpo with a least element.[1][2] It was introduced by Dito Pataraia in 1997.[3] The theorem is a variant of the Bourbaki–Witt theorem.
See also
References
- Paul Taylor, A Fixed Point Theorem for Categories [1]
- Jean Goubault-Larrecq, Bourbaki, Witt, and Dito Pataraia, [2]
- Andrej Bauer, Peter LeFanu Lumsdaine, On the Bourbaki-Witt Principle in Toposes, Math. Proc. Cam. Phil. Soc. 155 (2013), no. 1, 87–99 doi:10.1017/S0305004113000108, arXiv:1201.0340. [3]
- Martin Escardo. Joins in the frame of nuclei. Applied Categorical Structures 11: 117–124, 2003. https://doi.org/10.1023/A:1023555514029
- https://martinescardo.github.io/TypeTopology/Various.Pataraia.html
Further reading
- https://ncatlab.org/nlab/show/fixed+point#pataraias_theorem
- https://golem.ph.utexas.edu/category/2012/10/the_curious_dependence_of_set.html#c042391
- ↑ Template:Harvnb
- ↑ Example 6.7.12. in Template:Cite book, nlab entry at [4]
- ↑ Dito Pataraia. A constructive proof of Tarski’s fixed-point theorem for dcpo’s. Presented in the 65th Peripatetic Seminar on Sheaves and Logic, in Aarhus, Denmark, November 1997.