Visual Category Theory

Concepts from category theory were used as metaphors for some trace and log analysis patterns (see Mathematical Concepts in Software Diagnostics and Software Data Analysis) and also as a foundation of software diagnostics (see Categorical Foundations of Software Diagnostics) as a part of Theoretical Software Diagnostics. However, 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® bricks. This method was discovered when applying the same technique to teach machine learning, its data structures and algorithms, particularly directed graphs.

In order to facilitate earlier adoption and feedback, the book was split into small manageable parts. Part 1 (ISBN-13: 978-1912636402) is currently available on Leanpub and Amazon Kindle Store. It covers the definition of categories, arrows, the composition and associativity of arrows, retracts, equivalence, covariant and contravariant functors, natural transformations, and 2-categories.


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Part 2 (ISBN-13: 978-1912636419) is currently available on Leanpub and Amazon Kindle Store. It covers duality, products, coproducts, biproducts, initial and terminal objects, pointed categories, matrix representation of morphisms, and monoids.


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Part 3 (ISBN-13: 978-1912636426) is currently available on Leanpub and Amazon Kindle Store. It covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks and pushouts.


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Part 4 (ISBN-13: 978-1912636433) is currently available on Leanpub and Amazon Kindle Store. It covers non-concrete categories, group objects, monoid, group, opposite, arrow, slice, and coslice categories, forgetful functors, monomorphisms, epimorphisms, and isomorphisms.


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Part 5 (ISBN-13: 978-1912636440) is currently available on Leanpub and Amazon Kindle Store. It 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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Part 6 (ISBN-13: 978-1912636457) is currently available on Leanpub and Amazon Kindle Store. It covers ideas that require a leap of abstraction: vertical and whisker compositions of natural transformations, identity and isomorphism of functors, equivalence, isomorphism, and adjoint equivalence of categories, functor and morphism categories, natural transformations as functors, representable functors, category of presheaves, Yoneda embedding and lemma. It also includes an index for parts 1 - 6.


Book Sample

The first 5 parts are available as Visual Category Theory bundle on Leanpub.

Applications of category theory to software diagnostics also include Software Codiagnostics and Diagnostic Operads.