Descriere & specificații

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 utilizes a novel approach to teach category theory and abstract mathematics in general by using LEGO(R) bricks. This method was discovered when applying the same technique to teach machine learning, its data structures and algorithms, particularly directed graphs. This book can also be used as a diagrammatic reference for concepts of category theory. Part 0 covers universe and sets, set-builder notation, set membership, set inclusion, subsets as members, membership vs. subset, powerset, relations, functions, domain, codomain, range, injection, surjection, bijection, product, union, intersection, set difference, symmetric set difference, sets of functions, function composition, inverse functions. 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, arr