The joy of abstraction: an exploration of math, category theory, and life

Prologue: The status of mathematics ; Traditional mathematics : subjects ; Traditional mathematics : methods ; The content in this book ; Audience

Building Up to Categories. Categories : the idea

Abstraction

Patterns

Context

Relationships

Formalism

Equivalence relations

Categories : the definition

Interlude : a tour of math

Examples we've already seen, secretly

Ordered sets

Small mathematical structures

Sets and functions

Large worlds of mathematical structures

Doing Category Theory. Isomorphisms

Monics and epics

Universal properties

Duality

Products and coproducts

Pullbacks and pushouts

Functors

Categories of categories

Natural transformations

Yoneda

Higher dimensions

Epilogue: Thinking categorically

Appendices: Background on alphabets ; Background on basic logic ; Background on set theory ; Background on topological spaces.