Seven Sketches in Compositionality Quotes

“while many real-world structures are compositional, the results of observing them are often not. The reason is that observation is inherently “lossy”: in order to extract information from something, one must drop the details.”
― Brendan Fong, An Invitation to Applied Category Theory: Seven Sketches in Compositionality

“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