Steps Towards Diamond Category Theory

The story of developing diamond theory is going on quite well.
I just published a draft chapter of The Book of Diamonds:

Steps Towards Diamond Category Theory
http://www.thinkartlab.com/pkl/lola/Diamond-Category-Theory.pdf

Experimental Sketch 0.1

Steps Towards a Diamond Category Theory
1 Options of graphematic thematizations
1.1 Mono-contextural thematizations 1
1.2 Polycontextural thematizations 1
1.3 Diamond thematizations 1
1.4 Prospect of Diamond Theory 3

2 Diamonds and Contextures
2.1 Laws for sets 7
2.2 Laws for classes 7
2.3 Laws for conglomerates 7
2.4 Laws for universes 7
2.5 Laws for chiasms between universes 7

3 Object-based Category Theory
3.1 Description of the intuition 9
3.2 Diamond composition 10
3.3 Diamond Associativity 13

4 Object-free categories
4.1 Matching conditions 15
4.2 In-sourcing the matching conditions 18

5 Properties of diamonds
5.1 Diamond rules for morphisms 22
5.2 Sub-Diamonds 24
5.3 Diamond products 25
5.4 Terminal and initial objects in diamonds 26
5.5 Functors between diamonds 27
5.6 Natural Transformation and Diamonds 28

6 Aspects of diamonds
6.1 Data, Structure, Property (DSP) for Categories 32
6.2 Data, Structure, Property, Interactionality (DSPI)
for Diamonds 32
6.3 Diamondization of diamonds 34
6.4 Conceptual graphs of higher-order diamondizations 35

7 Axiomatizations of Diamonds
7.1 Axiomatics One 70

8 Complexity reduction by diamondization 72
8.1 Reduction steps 72
8.2 Reduction by morphograms 73
8.3 Diamonds as complementations of Categories 74

Overview
http://www.thinkartlab.com/pkl/PDF-Overview/PDF-Overview.html