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Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/context.pdf and is being updated regularly. The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.

9 July 2017 Edit. Updated the link to the text.

Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/context.pdf and errata in the published version are being updated. The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.

9 July 2017 Edit. Updated the link to the text.

Emily Riehl's forthcoming book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/727/context.pdf and is being updated regularly. The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.

Emily Riehl's recently published book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/context.pdf and is being updated regularly. The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.

9 July 2017 Edit. Updated the link to the text.

Emily Riehl's forthcoming book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some exposure to algebra and topology, but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/727/context.pdf and is being updated regularly. The text is new so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.

Emily Riehl's forthcoming book Category theory in context is a fantastic introductory text for those interested in seeing lots of examples of where category theory arises in various mathematical disciplines. Understand the examples from other branches of mathematics requires some mathematical maturity (e.g., a bit of exposure to algebra and topology), but these examples aren't strictly necessary to understand the category theory; even the less advanced reader should have no problem understanding the categorical content of the text. It stresses the importance of representability, an understanding of which is crucial if the reader wants to go on to learn about $ 2 $-categories in the future. It's elegantly written, well-motivated, uses very clear notation, and overall is refreshingly clear in its exposition.

The current version of the text is available at http://www.math.jhu.edu/~eriehl/727/context.pdf and is being updated regularly. The text is new, so it's not as well-known as other texts, but it's so well-written that it seems very likely that it will soon become a mainstay in the world of category theory texts.