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# Applied Category Theory - Syllabus

edited March 2020

Now that the MIT 2020 course is over, let's keep our ACT study efforts going! See the forum category that this discussion belongs to.

Syllabus.

MIT 2020 Programming with Categories course:

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Comment Source: - [Bartosz Milewski's Blog](https://bartoszmilewski.com/) - [_Categories For Programmers_](https://github.com/hmemcpy/milewski-ctfp-pdf/releases/download/v1.3.0/category-theory-for-programmers.pdf), which is selection of Bartosz's blog posts - The [Comonad Reader Blog](http://comonad.com/reader/) - [Philip Freeman's Blog](https://blog.functorial.com/) - Papers - [Wadler, _Theorems For Free!_ (1989)](https://ecee.colorado.edu/ecen5533/fall11/reading/free.pdf) - [Meijer et al, _Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire_ (1991)](https://maartenfokkinga.github.io/utwente/mmf91m.pdf) - [Wadler, _Comprehending Monads_ (1990)](https://ncatlab.org/nlab/files/WadlerMonads.pdf) - [Moggi, _Notions of Computation as Monads_ (1995)](https://core.ac.uk/download/pdf/21173011.pdf) - [Rutten, _Automata and Coinduction (an exercise in coalgebra)_ (1998)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.221.6957&rep=rep1&type=pdf) - [McBridge et. al, _Applicative Programming With Effects_ (2008)](https://openaccess.city.ac.uk/id/eprint/13222/1/) - [Hinze, _Reason Isomorphically!_, (2010)](http://www.cs.ox.ac.uk/people/daniel.james/iso/iso.pdf) - [Pickering et. al, _Profunctor Optics_ (2012)](https://arxiv.org/ftp/arxiv/papers/1703/1703.10857.pdf) - [Rivas et al., _Notions of Computation as Monoids_ (2014)](https://arxiv.org/pdf/1406.4823.pdf) - [Jaskelioff, _A Representation Theorem For Second Order Functionals_ (2014)](https://arxiv.org/pdf/1402.1699.pdf) - Haskell Libraries - [kan-extensions](https://hackage.haskell.org/package/kan-extensions) - [fmlist](https://hackage.haskell.org/package/fmlist) - [mmorph](https://hackage.haskell.org/package/mmorph) - [free-categories](http://hackage.haskell.org/package/free-categories-0.1.0.0) - John Wiegley's [coq-category](https://github.com/jwiegley/category-theory), which isn't in Haskell but is a great formulation of category theory in a pure functional language
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edited February 2020

Written during the MIT 2019 course on ACT.

Comment Source:* John Baez, [77 lectures on applied category theory](https://forum.azimuthproject.org/categories/mit-2019%3A-lectures), Azimuth Forum, 2019. Written during the MIT 2019 course on ACT.
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edited February 2020
Comment Source:* Michael Barr and Charles Wells, [Category theory for computing science (1998)](http://bit.ly/37y54Tb) * Michael Barr and Charles Wells, [Toposes, triples and theories (1985, 2005)](http://bit.ly/39MvdiD)
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edited February 2020
• Sanders Mac Lane, Categories for the Working Mathematician, Springer, 1971.

• Benjamin C. Pierce, Basic Category Theory for Computer Scientists, MIT Press, 1991.

• Emily Riehl, Category Theory in Context, Courier Dover Publications, 2016.

• David Spivak, Category Theory for the Sciences, MIT Press, 2014.

• Bartosz Milewski, Category Theory for Progammers, Blurb Inc., 2019.

Comment Source:* Sanders Mac Lane, _Categories for the Working Mathematician_, Springer, 1971. * Benjamin C. Pierce, _Basic Category Theory for Computer Scientists_, MIT Press, 1991. * Emily Riehl, _Category Theory in Context_, Courier Dover Publications, 2016. * David Spivak, _Category Theory for the Sciences_, MIT Press, 2014. * Bartosz Milewski, _Category Theory for Progammers_, Blurb Inc., 2019. 
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edited February 2020
Comment Source:* [Applied category theory](http://math.ucr.edu/home/baez/ACTUCR2019/), AMS Western Sectional Meeting, 9-10 November 2019, U.C. Riverside. * [Applied category theory](http://math.ucr.edu/home/baez//ACT2017/), AMS Western Sectional Meeting, 4-5 November 2017, U.C. Riverside.
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6.

John C. Baez and Brendan Fong, A Compositional Framework for Passive Linear Networks, arXiv:1504.05625v6 [math.CT], Nov 2018.

Comment Source:John C. Baez and Brendan Fong, [A Compositional Framework for Passive Linear Networks](https://arxiv.org/abs/1504.05625), arXiv:1504.05625v6 [math.CT], Nov 2018.
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Brent Yorgey's Typeclassopedia provides a useful conceptual hierarchy of Haskell types.

Comment Source:Brent Yorgey's Typeclassopedia provides a useful conceptual hierarchy of Haskell types. * https://wiki.haskell.org/Typeclassopedia 
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Comment Source:Paulo Perrone, [Notes on Category Theory with examples from basic mathematics (2020)](https://arxiv.org/abs/1912.10642) 
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Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Roman, Profunctor optics (2020)

Comment Source:Bryce Clarke, Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore and Mario Roman, [Profunctor optics (2020)](https://arxiv.org/pdf/2001.07488.pdf)
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edited March 2020

Jim suggested this text:

Paulo Perrone, Notes on Category Theory with examples from basic mathematics (2020)

This has a very good introduction for scientists and engineers interested in data-flow approaches. Coincidental that Perrone chooses a rare construction to introduce a composite

The highlighted text is rare because the units of the inner and outer terms both have to be in radians. I have been using this formulation in the ENSO&QBO Azimuth Forum thread where it comes out of a Navier-Stokes LTE closed-form solution.

This is the composite data-flow:

I mentioned a possible connection to applied Category Theory in this earlier comment: https://forum.azimuthproject.org/discussion/comment/21098/#Comment_21098

Where else this sin(cos(x)) formulation comes up in is in Mach-Zehnder modulation, where the physical data flow is described by a beam splitter, which mathematically transforms into a composite of a sinusoidally modulated inner phase term.

more detail here: https://geoenergymath.com/2020/03/02/australia-bushfire-causes/

Comment Source:Jim suggested this text: > Paulo Perrone, Notes on Category Theory with examples from basic mathematics (2020) This has a very good introduction for scientists and engineers interested in data-flow approaches. Coincidental that Perrone chooses a rare construction to introduce a composite > ![](http://imageshack.com/a/img923/8991/QaxMhz.png) The highlighted text is rare because the units of the inner and outer terms both have to be in radians. I have been using this formulation in the ENSO&QBO Azimuth Forum thread where it comes out of a Navier-Stokes LTE closed-form solution. This is the composite data-flow: ![](https://imagizer.imageshack.com/img924/8215/ycXSL8.png) I mentioned a possible connection to applied Category Theory in this earlier comment: https://forum.azimuthproject.org/discussion/comment/21098/#Comment_21098 Where else this sin(cos(x)) formulation comes up in is in [Mach-Zehnder modulation](https://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer), where the physical data flow is described by a beam splitter, which mathematically transforms into a composite of a sinusoidally modulated inner phase term. > ![](https://www.researchgate.net/profile/Deepak_Sharma185/publication/319738972/figure/fig4/AS:538712769810432@1505450541525/Block-diagram-of-Mach-Zehnder-modulator.png) more detail here: https://geoenergymath.com/2020/03/02/australia-bushfire-causes/