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® 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.