[FRIAM] Applied Category Theory 2021 — Adjoint School – Azimuth

[Frank Wimberly]

Thanks, Roger, that works.  I also found a book by Leinster there called
"Basic Category Theory" which looks ideal for me.  A PDF is available for
free but I will probably order the hardcopy version.

Frank

On Mon, Jan 4, 2021 at 11:06 AM Roger Frye <frye.roger at gmail.com> wrote:

> Looks like results of previous classes were supposed to be written up at
> the n-category-cafe.
>
>
> On Mon, Jan 4, 2021 at 10:57 AM Frank Wimberly <wimberly3 at gmail.com>
> wrote:
>
>> Do I understand correctly that there are 4 or 5 projects and 4 members of
>> each project.  I think I'll leave this for younger people like you Jon.
>> Are the presentations and results available online?
>>
>> Frank
>>
>> On Mon, Jan 4, 2021 at 9:37 AM jon zingale <jonzingale at gmail.com> wrote:
>>
>>> cool. This topic looks particularly good:
>>>
>>> Topic: Extensions of coalgebraic dynamic logic
>>> Mentors: Helle Hvid Hansen and Clemens Kupke
>>>
>>> Description: Coalgebra is a branch of category theory in which different
>>> types of state-based systems are studied in a uniform framework,
>>> parametric
>>> in an endofunctor F:C → C that specifies the system type. Many of the
>>> systems that arise in computer science, including
>>> deterministic/nondeterministic/weighted/probabilistic automata, labelled
>>> transition systems, Markov chains, Kripke models and neighbourhood
>>> structures, can be modeled as F-coalgebras. Once we recognise that a
>>> class
>>> of systems are coalgebras, we obtain general coalgebraic notions of
>>> morphism, bisimulation, coinduction and observable behaviour.
>>>
>>> Modal logics are well-known formalisms for specifying properties of
>>> state-based systems, and one of the central contributions of coalgebra
>>> has
>>> been to show that modal logics for coalgebras can be developed in the
>>> general parametric setting, and many results can be proved at the
>>> abstract
>>> level of coalgebras. This area is called coalgebraic modal logic.
>>>
>>> In this project, we will focus on coalgebraic dynamic logic, a
>>> coalgebraic
>>> framework that encompasses Propositional Dynamic Logic (PDL) and Parikh’s
>>> Game Logic. The aim is to extend coalgebraic dynamic logic to system
>>> types
>>> with probabilities. As a concrete starting point, we aim to give a
>>> coalgebraic account of stochastic game logic, and apply the coalgebraic
>>> framework to prove new expressiveness and completeness results.
>>>
>>> Participants in this project would ideally have some prior knowledge of
>>> modal logic and PDL, as well as some familiarity with monads.
>>>
>>>
>>>
>>> --
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>>>
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>>
>>
>> --
>> Frank Wimberly
>> 140 Calle Ojo Feliz
>> Santa Fe, NM 87505
>> 505 670-9918
>>
>> Research:  https://www.researchgate.net/profile/Frank_Wimberly2
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>>
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-- 
Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918

Research:  https://www.researchgate.net/profile/Frank_Wimberly2
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