morphisms-of-computational-structures

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Leads: https://twitter.com/_Pablo_Morales/status/1435253700268728324 First paper: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033216 https://twitter.com/_fernando_rosas/status/1508364933490253827 Second paper: https://arxiv.org/abs/2203.13673 Legendre transform and geometry: https://link.springer.com/article/10.1007/s41884-018-0012-6 Think this connects with optimal transport https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.033216 Categorical origins of entropy https://twitter.com/RAnachro/status/1221851414550515714 https://www.youtube.com/watch?v=JgNy2ZUqdZI https://twitter.com/enclanglement/status/1495443960071917570 https://twitter.com/johncarlosbaez/status/1521859058227056641

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A curation on some reads in the direction of non-wellfoundedness with emphasis on their significance for mathematical foundations. ### 1/ Sets as Graphs Alexander Ioan Tomescu (2011) https://www.cs.helsinki.fi/u/tomescu/PhDThesis-AT.pdf A thesis...

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Mathematical theories of abstractions

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What is abstraction? There are three ways to see this: 1/ Creating equivalences (quotienting / equivalence classes) 2/ Focussing on what is important and ignoring the unimportant 3/ Creating a...

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Trace the history of origin of operational and denotational semantics

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Plotkin’s account of the origin of Structural Operational Semantics: https://homepages.inf.ed.ac.uk/gdp/publications/Origins_SOS.pdf Dana Scott’s ACM Turing Award Lecture: https://amturing.acm.org/award_winners/scott_1193622.cfm

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Find out how the categorical duality between expressions and continuations can be grounded using initial and final algebras and co-algebras

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Lectures on Semantics: The initial algebra and final coalgebra perspectives Peter Aczel (1997) A Tutorial on (Co)Algebras and (Co)Induction: https://fldit-www.cs.tu-dortmund.de/~peter/JR.pdf Bart Jacobs, Jan Rutten (1997)

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Investigate bisimulation as a logical relation

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https://arxiv.org/pdf/2003.13542.pdf

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Examine this paper: On the Origins of Bisimulation and Coinduction

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http://www.cs.unibo.it/~sangio/DOC_public/history_bis_coind.pdf Discussion here: http://lambda-the-ultimate.org/node/2522

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[The Mathematics of Sentence Structure (1958)](https://www.cs.cmu.edu/~fp/courses/15816-f16/misc/Lambek58.pdf)

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Understand how coalgebra helps in modal logic

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Paper: https://eprints.soton.ac.uk/262612/

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Call by Push Value by Paul Blain Levy Duality between Call by Value and Call by Name: https://homepages.inf.ed.ac.uk/wadler/papers/dual/dual.pdf

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