###### Visual Category Theory

# Visual Category Theory

# About the Bundle

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. Part 1 covers the definition of categories, arrows, the composition and associativity of arrows, retracts, equivalence, covariant and contravariant functors, natural transformations, and 2-categories. Part 2 covers duality, products, coproducts, biproducts, initial and terminal objects, pointed categories, matrix representation of morphisms, and monoids. Part 3 covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks and pushouts. Part 4 covers non-concrete categories, group objects, monoid, group, opposite, arrow, slice, and coslice categories, forgetful functors, monomorphisms, epimorphisms, and isomorphisms. Part 5 covers exponentials and evaluation in sets and categories, subobjects, equalizers, equivalence classes and quotients, coequalizers, congruence categories, morphism functors, and presheaves.

#### About the Books

### Visual Category Theory Brick by Brick, Part 1

###### Using LEGO® to Teach Abstract Mathematics

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. This part includes representation of categories, arrows, the composition and associativity of arrows, retracts, equivalence, covariant and contravariant functors, natural transformations, and 2-categories.

### Visual Category Theory Brick by Brick, Part 2

###### Using LEGO® to Teach Abstract Mathematics

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. The second part covers duality, products, coproducts, biproducts, initial and terminal objects, pointed categories, matrix representation of morphisms, and monoids.

### Visual Category Theory Brick by Brick, Part 3

###### Using LEGO® to Teach Abstract Mathematics

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. The third part covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks and pushouts.

### Visual Category Theory Brick by Brick, Part 4

###### Using LEGO® to Teach Abstract Mathematics

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. The fourth part covers non-concrete categories, group objects, monoid, group, opposite, arrow, slice, and coslice categories, forgetful functors, monomorphisms, epimorphisms, and isomorphisms.

### Visual Category Theory Brick by Brick, Part 5

###### Using LEGO® to Teach Abstract Mathematics

Category theory abstractions are very challenging to apprehend correctly, require a steep learning curve for non-mathematicians, and, for people with traditional naïve set theory education, a paradigm shift in thinking. The book uses LEGO® to teach category theory. The fifth part covers exponentials and evaluation in sets and categories, subobjects, equalizers, equivalence classes and quotients, coequalizers, congruence categories, morphism functors, and presheaves.

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