Problem based category-theory book.

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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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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.