Visual Category Theory, CoPart 1: A Dual to Brick by Brick, Part 1

This CoPart is a dual complement to Visual Category Theory Brick by Brick, Part 1. The original series translated abstract categorical concepts into the language of LEGO(R) bricks, and the CoPart series implement the opposite way of translating brick constructions to the standard diagram language of category theory that should benefit comprehension of definitions.

Since usual categorical diagrams are black and white and occupy less space on paper, CoParts include additional color-enhanced diagrams in the spirit of brick constructions when arrow source and target parts use different colors.

These CoParts from CoSeries (named after opposite categories with reversed arrows) keep the same 1-to-1 page correspondence between Parts and CoParts. Page layout is also similar: location of explanatory notes (written using standard mathematical notation) is the same - only bricks are replaced by letters, dots, and arrows. Therefore, this CoSeries can be used independently from the original series or together.

The first CoPart covers the definition of categories, arrows, the composition and associativity of arrows, retracts, equivalence, covariant and contravariant functors, natural transformations, and 2-categories.

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, and 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, and applications of category theory to software development and big data.