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

Using LEGO® to Teach Abstract Mathematics

About the Book

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.

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About the Author

Dmitry Vostokov
Dmitry Vostokov

Dmitry Vostokov is an internationally recognized expert, speaker, educator, scientist, inventor, and author. He is the founder of pattern-oriented software diagnostics, forensics, and prognostics discipline (Systematic Software Diagnostics), and Software Diagnostics Institute. Vostokov has also authored more than 50 books on software diagnostics, anomaly detection and analysis, software and memory forensics, root cause analysis and problem solving, memory dump analysis, debugging, software trace and log analysis, reverse engineering and malware analysis. He has more than 25 years of experience in software architecture, design, development and maintenance in a variety of industries including leadership, technical and people management roles. Dmitry also founded Syndromatix, Anolog.io, BriteTrace, DiaThings, Logtellect, OpenTask Iterative and Incremental Publishing, Software Diagnostics Technology and Services (former Memory Dump Analysis Services), and Software Prognostics. In his spare time, he presents various topics on Debugging TV and explores Software Narratology, its further development as Narratology of Things and Diagnostics of Things (DoT), Software Pathology, and Quantum Software Diagnostics. His current areas of interest are theoretical software diagnostics and its mathematical and computer science foundations, application of formal logic, artificial intelligence, machine learning and data mining to diagnostics and anomaly detection, software diagnostics engineering and diagnostics-driven development, diagnostics workflow and interaction. Recent interest areas also include cloud native computing, security, automation, functional programming, applications of category theory to software diagnostics, development and big data, and diagnostics of artificial intelligence.

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Table of Contents

Definition of category

Compositionality of arrows

Associativity

Identity arrow

Equivalence

Section and retraction

Covariant functor

Contravariant functor

Natural transformation

2-Category

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