Category Theory Quotes

“The language of categories is affectionately known as "abstract nonsense," so named by Norman Steenrod. This term is essentially accurate and not necessarily derogatory: categories refer to "nonsense" in the sense that they are all about the "structure," and not about the "meaning," of what they represent.”
― Paolo Aluffi, Algebra: Chapter 0

“Note that in the above construction we made a number of choices; here we must beware. Choosing a good categorification – like designing a good algebraic structure such as that of preorders or quantales – is part of the art of mathematics. There is no prescribed way to categorify, and the success of a chosen categorification is rather empirical: its richer structure should allow us more insights into the subject we want to model.”
― Brendan Fong, Seven Sketches in Compositionality: An Invitation to Applied Category Theory