http://meng6net.localhost/tag/category_theory/ <p><small>Copyright © 2005-2020 by <code>Meng Lu &lt;lumeng3@gmail.com&gt;</code></small></p> Meng Lu's home page ikiwiki Tue, 16 May 2017 21:31:58 +0000 http://meng6net.localhost/journal/category_theory_note/ http://meng6net.localhost/journal/category_theory_note/ category theory mathematics programming to-do Tue, 11 Apr 2017 07:18:07 +0000 2017-05-16T21:31:58Z <h2>Draft</h2> <ul> <li> <p><a href= "https://en.wikipedia.org/wiki/Multigraph">multigraph</a></p> </li> <li> <p>quiver graph: directed multigraph, 有向伪图</p> </li> <li> <p>quiver, loop arrows from and to the same vertex</p> </li> <li> <p>object, vertex in a graph</p> </li> <li> <p>from directed multigraph to categories</p> </li> <li> <p>morphism, or arrow</p> </li> <li> <p>identity morphism</p> </li> <li> <p>composition of morphisms</p> </li> <li> <p>There can be multiple different loops on one object, but one of them must be the identity morphism. Why?</p> </li> <li> <p>endofunctor</p> </li> <li> <p>Haskell languge is a category, Hask, with the Haskell language types as the objects and Haskell-langauge functions are morphisms.</p> </li> <li> <p>'Hask' is a Cartesian closed category</p> </li> <li> <p>n-category</p> </li> <li> <p>monoids for input and output in Haskell language</p> </li> </ul> <h2>Topics</h2> <ul> <li> <p>Haskell and WL</p> </li> <li> <p>category theory and WL</p> </li> </ul> <h2>References</h2> <ul> <li>Bartosz Milewsk, "Category Theory for Programmers," 2014 - 2017, https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/.</li> <li><a href="http://cheng.staff.shef.ac.uk/research.html">Eugenia Cheng's research papers on category theory</a></li> <li><a href= "https://www.youtube.com/user/TheCatsters">'TheCatsters' Youtube channel</a> <ul> <li><a href="https://byorgey.wordpress.com/catsters-guide-2/">Brent Yorgey's index to 'TheCatsters' videos</a></li> </ul> </li> <li>Tom Leinster, "Basic Category Theory," 2016, <a href= "https://arxiv.org/pdf/1612.09375.pdf">arXiv:1612.09375v1 [math.CT]</a></li> <li><a href= "https://arxiv.org/find/math/1/au:+Leinster_T/0/1/0/all/0/1">Tom Leinster's research papers</a></li> </ul>