# Exercises from Seven Sketches in Compositionality: An Invitation to Applied Category

## Exercise 1.1

• (a) $f(x) = 2x$ is order preserving, $f(x) = x^2$ is not.
• (b) $f(x) = \frac{1}{x}$ is metric-preserving, $f(x) = -x$ is not.
• (c) $f(x) = x + 1$ is addition-preserving, $f(x) = |x|$ is not.