Crossed homomorphism

Connected affine group scheme 51 Connected component of G 51 Connected set, connected component 157 Constant group scheme 16, 45 Continuous function 157 Continuous -action 48 Coseparable coalgebra 53 Crossed homomorphism 137... 

Clearly we can define these concepts using just the T-action. Let T be any group acting as automorphisms of a group F. The maps / T - F satisfying f at) =/(equivalence relation in general. The set of equivalence classes is denoted // (T, F). 

Within each quartet, the morphic relationship between any pair of circles (representing distinct conjunctive states) is marked by an arc or a cross-link (arcs are for mi-to-mi-, mi-to-m2, mi -to-m2, and m2-to-m2 cross-links are for mi-to-my and mi-to-m2). Once the morphic relationships for the arcs are picked, those for the cross-links follow suit. The arcs and crosslinks are drawn very thick, thick, and thin for homomorphic, enantiomorphic, and diastereomorphic relationships, respectively the arcs and cross-links are dashed and dotted for astereomorphic and nonequimorphic relationships, respectively. For a given quartet of circles, every arc or cross-link may reflect any one of the five fundamental morphic relationships (Figure 12.4). 

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