"Thinking with categories" a small introduction for the layman.
May be a more commercial title would be "Functorial Thinking".
A small book (circa 120 p.) with the goal of explaining basic category theory using plenty of examples but mostly non mathematical ones.
Intended for an audience of linguists, philosophers, computer designers and any curious intellectual.
The book presuppose a reader not adverse to a minimum of algebra, yet it should mostly contains basic defining algebraic equations for categories, functors , natural transformations and adjunctions.
The goal of this book: It should enable a philosopher (not necessarily specialized in logic) to grasp properly what an adjunction is in 2 to 4 hours.
The basic motivation: Find proper real-life examples (as in elementary set theory) for category theory.
To illustrate : A 5-subset of a football team can be made by picking some players randomly, but a sub-object is a set of 5 players that can play together! In fact common language would call it sub-team. So far when trying to design examples in real life you end up too often with groupoids and thin category(posets).
Any suggestions of places from which to draw material/inspiration would be most welcome.
