Definition of category
Compositionality of arrows
Associativity
Identity arrow
Equivalence
Section and retraction
Covariant functor
Contravariant functor
Natural transformation
2-Category
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.
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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.
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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 is an internationally recognized expert, speaker, educator, scientist, inventor, and author. He founded the pattern-oriented software diagnostics, forensics, and prognostics discipline (Systematic Software Diagnostics) and Software Diagnostics Institute. Vostokov has also authored over 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 over 30 years of experience in software architecture, design, development, and maintenance in various industries, including leadership, technical, and people management roles. Dmitry founded OpenTask Iterative and Incremental Publishing and Software Diagnostics Technology and Services (former Memory Dump Analysis Services). In his spare time, he explores Software Narratology and Quantum Software Diagnostics. His interest areas are theoretical software diagnostics and its mathematical and computer science foundations, application of formal logic, semiotics, 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 functional programming, cloud native computing, monitoring, observability, visualization, security, automation, applications of category theory to software diagnostics, development and big data, and diagnostics of artificial intelligence.
Episode 213
An Interview with Dmitry Vostokov
Contents
Table of Contents
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