
Preface v
Abbreviations xix
1. Introduction 1
1.1 Diversifying and Unifying Ways 1
1.2 Categorifi cation and Decategorifi cation 3
1.3 Polytope Projects 7
References 14
2. Methods and Models 17
2.1 Differential Posets 17
2.2 Dual Graded Graphs 21
2.3 Updown Categories 24
2.4 Combinatorial Species 26
2.5 Polytopes and n-Levels Systems 33
2.6 Differential Models 35
2.6.1 Modeling Differential Posets 35
2.6.2 Derivative Complexes 36
2.6.3 Differential Ring of Polytopes 37
2.6.4 Combinatorial Differential Calculus 38
2.6.5 Generic Models 41
References 44
3. Separation and Integration 47
3.1 Binary Rooted Trees for Separation 47
3.1.1 Separation ...