I love problem based textbooks like all of those by R. P. Burn and Halmos' Linear Algebra Problem Book, etc. Are there any problem based Category Theory textbooks, I know that the first chapters of Modern Classical Homotopy Theory by Strom can count, but I want a more general one.
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Perhaps a dive through http://math.stackexchange.com/questions/370/good-books-and-lecture-notes-about-category-theory may help? – Ken Jun 25 '15 at 14:34
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Perhaps you can try taking a classic (e.g. Categories for the working mathematician) and try to prove all the theorems yourself. – Zhen Lin Jun 25 '15 at 16:57
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1I believe that the answer is "No". – Martin Brandenburg Jun 25 '15 at 20:58
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David Spivak's Category Theory for the Sciences has lots of great examples (with solutions depending on your edition) that comes about as close to such a text as you're likely to find. It rides a fine line between mathematics and engineering/sciences with a stronger foot in mathematics. Keep in mind that there are multiple versions of his "open" text available on the interwebs.
Chris Aldrich
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Spivak also put out one more recently with Brendan Fong with a long name, but it's applied category theory and is dense with examples and exercises, and gives all of the solutions in the end of the book. Each chapter progresses in a cool way in terms of difficulty. They made a chart for it. And, each chapter has an overall theme of application from different areas of study and industry application, with a lot of examples of widely varying application throughout each chapter as well!
There are lectures to go with it on Youtube from two different semesters, the second being more complete. Here's the full playlist of the latter https://www.youtube.com/watch?v=UusLtx9fIjs&list=PLhgq-BqyZ7i5lOqOqqRiS0U5SwTmPpHQ5
There is also an online course that John Baez based on the book that is still accessible and still has some activity I think: https://forum.azimuthproject.org/categories/applied-category-theory-course
There is also an open courseware site at MIT: https://ocw.mit.edu/courses/mathematics/18-s097-applied-category-theory-january-iap-2019/
user3146
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