These texts can work as an introductory undergraduate sequence (with “Sets for Mathematics” going after enough exposure to rigor, e.g. a real analysis course, maybe some set theory and logic, and Awodey’s book after a bit of abstract algebra, maybe functional programming with types, as in Haskell/Standard ML/etc.):
F. W. Lawvere & S. H. Schanuel (1991). Conceptual Mathematics: A First Introduction to Categories. Buffalo Workshop Press, Buffalo, NY, USA.
F. W. Lawvere & R. Rosebrugh (2003). Sets for Mathematics. Cambridge University Press.
S. Awodey (2006). Category Theory. Oxford Logic Guides. Oxford University Press, USA.
Second the recommendation of Lawvere and Schanuel. It really communicates the categorical way of thinking without requiring a lot of mathematical background (more traditional texts on category theory will talk about things like algebraic topology which historically motivated category theory but aren’t conceptually prior to it).
These texts can work as an introductory undergraduate sequence (with “Sets for Mathematics” going after enough exposure to rigor, e.g. a real analysis course, maybe some set theory and logic, and Awodey’s book after a bit of abstract algebra, maybe functional programming with types, as in Haskell/Standard ML/etc.):
F. W. Lawvere & S. H. Schanuel (1991). Conceptual Mathematics: A First Introduction to Categories. Buffalo Workshop Press, Buffalo, NY, USA.
F. W. Lawvere & R. Rosebrugh (2003). Sets for Mathematics. Cambridge University Press.
S. Awodey (2006). Category Theory. Oxford Logic Guides. Oxford University Press, USA.
Second the recommendation of Lawvere and Schanuel. It really communicates the categorical way of thinking without requiring a lot of mathematical background (more traditional texts on category theory will talk about things like algebraic topology which historically motivated category theory but aren’t conceptually prior to it).