## between

There cannot be two edges between one pair of vertices.

Generally we add a tilde to distinguish between quantities associated with $\tilde{G}$ and those associated with $G$.

It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.

The assignment of $K_1$ to $K$, and of $T_1$ to $T$, defines a functor between the category of commutative algebras and the category of compact semigroups with continuous homomorphisms.

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