Introduction
Chapter
I.
Groupoids
I.l.
Abstract Maps of Graphs
1.2. The Basic Operations
1.3. Free Groupoids
1.4. Inertia
1.5. The Fixed Subgroupoid
Chapter II. Measuring Devices
Contents
11.1. Some Aspects of the Perron-Frobenius Theorem
11.2. Metric Graphs and Weighted Graphs
11.3. The Five Quantifiers
Chapter III. Properties of the Basic Operations
111.1. Collapsing a Pretrivial Arc
111.2. Subdividing
111.3. Folding
111.4. Removing a Vertex of Valence Two
Chapter IV. Minimal Representatives and Fixed Subgroupoids
IV .1. Existence
IV.2. Smoothness
IV.3. Indivisible Fixed Elements
IV.4. Folding Indivisible Fixed Elements
IV.5. Inertia of the Fixed Subgroupoid
Open Problems
Bibliography
Index
ix
1
5
5
11
14
18
23
27
27
30
33
35
35
36
39
42
45
45
47
51
55
61
71
75
77
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