Abstract
In a recent note (Palmgren, 2005) Erik Palmgren has shown that, in a sufficiently strong version of Martin-Löf’s type theory (Martin-Löf, 1984) the category of set-presented formal topologies has coequalisers. We refer the reader to (Palmgren, 2005) for the background motivation for this result.
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Bibliography
Aczel, P. and Rathjen, M. (2001). Notes on constructive set theory. Technical Report 40, The Royal Swedish Academy of Sciences, Institut Mittag-Leffler. Available at http://www.ml.kva.se/ preprints/archive2000-2001.php
Martin-Löf, P. (1984). Intuitionistic Type Theory. Lecture Notes by Giovanni Sambin. Studies in Proof Theory. Bibliopolis, Napoli.
Palmgren, E. (2005). Quotient spaces and coequalisers in formal topology. Journal of Universal Computer Science, 11(12):1996–2007.
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Aczel, P. (2011). Equalisers of Frames in Constructive Set Theory. In: DeVidi, D., Hallett, M., Clarke, P. (eds) Logic, Mathematics, Philosophy, Vintage Enthusiasms. The Western Ontario Series in Philosophy of Science, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0214-1_11
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DOI: https://doi.org/10.1007/978-94-007-0214-1_11
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