<story><title>Applied Category Theory</title><url>https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/</url></story><parent_chain></parent_chain><comment><author>danharaj</author><text>David Spivak has done lots of cool work on applying category theory to many concrete systems like databases [1].&lt;p&gt;Brendan Fong has worked on applying category theory to things that act like interconnected networks, such as electrical circuits. This fits into a larger ambitious program that John Baez is part of to use category theory to understand physical systems that are still much too complicated to understand with current mathematical tools, such as ecosystems. Fong&amp;#x27;s thesis is on my reading list [2].&lt;p&gt;The two authors are doing great research, like this investigation of the algebra of backpropagation [3].&lt;p&gt;I really look forward to reading this too!&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;0904.2012&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;0904.2012&lt;/a&gt;&lt;p&gt;[2] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1609.05382&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1609.05382&lt;/a&gt;&lt;p&gt;[3] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1711.10455&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1711.10455&lt;/a&gt;</text></comment>
<story><title>Applied Category Theory</title><url>https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/</url></story><parent_chain></parent_chain><comment><author>jfaucett</author><text>This looks like a great resource. I really think the chapter difficulty idea is a good one and wish more math books adopted this approach.&lt;p&gt;On another pedagogical note and as someone who reads a lot of math texts, I wish math textbooks would spend way more time on introducing the intuition (geometrical if in any way possible) of the ideas before or simultaneous with going into the formulas, theorems, and details. This not only vastly improves comprehension but I find having a geometrical understanding ( even if rough and partially incorrect) greatly helps in me being able to later derive the same formulas and theorems.&lt;p&gt;Having written about various math topics over the years I know its much more difficult to follow this approach, so I don&amp;#x27;t blame anyone for not going out of their way to imbue intuition, but its still something I wish more mathematicians who teach would advocate for.</text></comment>