F. William Lawvere, Stephen H. Schanuel.
Conceptual Mathematics: a first introduction to categories.
CUP. 1997
In the last fifty years, the use of the notion of ‘category’
has led to a remarkable unification and simplification of mathematics.
Written by two of the best-known participants in this development,
Conceptual Mathematics is the first book to serve both as
a skeleton key to mathematics for the general reader or beginning student
and as an introduction to categories for computer scientists, logicians, physicists, linguists, etc.
While the ideas and techniques of basic category theory are useful throughout modern mathematics,
this book does not presuppose knowledge of specific fields
but rather develops elementary categories such as directed graphs
and discrete dynamical systems from the beginning.
The fundamental ideas are then illuminated in an engaging way by examples in these categories.