Bc. Vít Jelínek
Master's thesis
Type theory and its semantics
Type theory and its semantics
Abstract:
V práci zkoumáme kategorie s reprezentovatelnými šipkami (CwRs) -- potenciální odpověď na otázku "Co je to (závislá) teorie typů?" navrženou Taichim Uemurou v jeho dizertační práci. Dokazujeme, že 2-kategorie všech CwRs má různé dobré 2-kategoriální vlastnosti -- jedná se o dosažitelnou 2-kategorii s flexibilními limitami a bikolimitami. Díky těmto vlastnostem můžeme CwRs volně generovat kategoriemi …moreAbstract:
We examine categories with representable maps (CwRs) -- an answer to the question `What is a (dependent) type theory?' suggested by Taichi Uemura in his PhD thesis. We prove that the 2-category of CwRs has various good 2-categorical properties -- it is an accessible 2-category with flexible limits and bicolimits. Using this, we deduce that CwRs can be freely generated by categories with specified arrows …more
Language used: English
Date on which the thesis was submitted / produced: 21. 5. 2024
Identifier:
https://is.muni.cz/th/fl75q/
Thesis defence
- Date of defence: 21. 6. 2024
- Supervisor: doc. John Denis Bourke, PhD
- Reader: doc. Benno Van den Berg, PhD
Full text of thesis
Contents of on-line thesis archive
Published in Theses:- světu
Other ways of accessing the text
Institution archiving the thesis and making it accessible: Masarykova univerzita, Fakulta informatikyMasaryk University
Faculty of InformaticsMaster programme / field:
Theoretical computer science / Discrete algorithms and models
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