\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Introduction}}{5}{chapter.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Groupoids}}{7}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Groupoids: their elements and attributes}}{7}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }ConnectedGroupoid}}{7}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }ComponentsOfGroupoid}}{8}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }IsPermGroupoid}}{8}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}\leavevmode {\color {Chapter }GroupoidElement}}{9}{subsection.2.1.4}
\contentsline {subsection}{\numberline {2.1.5}\leavevmode {\color {Chapter }IsConnectedGroupoid}}{10}{subsection.2.1.5}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Subgroupoids}}{10}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }SubgroupoidByComponents}}{10}{subsection.2.2.1}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Stars, Costars and Homsets}}{11}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }ObjectStar}}{11}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}\leavevmode {\color {Chapter }IdentityElement}}{12}{subsection.2.3.2}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter }Left, right and double cosets}}{12}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}\leavevmode {\color {Chapter }RightCoset}}{12}{subsection.2.4.1}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Morphisms of Groupoids}}{14}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Morphisms to a connected groupoid}}{14}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }MorphismOfConnectedGroupoids}}{14}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }MorphismToConnectedGroupoid}}{15}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color {Chapter }IsomorphismNewObjects}}{16}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}\leavevmode {\color {Chapter }InclusionMappingGroupoids}}{16}{subsection.3.1.4}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }General Morphisms and composites}}{17}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }GroupoidMorphismByComponents}}{17}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }IsGroupoidMorphism}}{18}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }ImagesOfObjects}}{18}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}\leavevmode {\color {Chapter }Product}}{19}{subsection.3.2.4}
\contentsline {subsection}{\numberline {3.2.5}\leavevmode {\color {Chapter }InverseMorphism}}{19}{subsection.3.2.5}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Graphs of Groups and Groupoids}}{20}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Digraphs}}{20}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }FpWeightedDigraph}}{20}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Graphs of Groups}}{21}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }GraphOfGroups}}{21}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }IsGraphOfFpGroups}}{22}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color {Chapter }RightTransversalsOfGraphOfGroups}}{23}{subsection.4.2.3}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }Words in a Graph of Groups and their normal forms}}{23}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }GraphOfGroupsWord}}{23}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }ReducedGraphOfGroupsWord}}{24}{subsection.4.3.2}
\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter }Free products with amalgamation and HNN extensions}}{24}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }FreeProductWithAmalgamation}}{24}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}\leavevmode {\color {Chapter }HnnExtension}}{26}{subsection.4.4.2}
\contentsline {section}{\numberline {4.5}\leavevmode {\color {Chapter }GraphsOfGroupoids and their Words}}{27}{section.4.5}
\contentsline {subsection}{\numberline {4.5.1}\leavevmode {\color {Chapter }GraphOfGroupoids}}{27}{subsection.4.5.1}
\contentsline {subsection}{\numberline {4.5.2}\leavevmode {\color {Chapter }GraphOfGroupoidsWord}}{28}{subsection.4.5.2}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Development History}}{29}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Versions of the Package}}{29}{section.5.1}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }What needs to be done next?}}{29}{section.5.2}
