Changes

In thinking about mappings between categories of structured individuals, we can take each mapping in two parts.  At the first level of analysis, there is the part that maps individuals to individuals.  At the second level of analysis, there is the part that maps the structural parts of each individual to the structural parts of the individual that forms its counterpart under the first part of the mapping in question.

In thinking about mappings between categories of structured individuals, we can take each mapping in two parts.  At the first level of analysis, there is the part that maps individuals to individuals.  At the second level of analysis, there is the part that maps the structural parts of each individual to the structural parts of the individual that forms its counterpart under the first part of the mapping in question.

The general scheme of things is suggested by the following Figure, where the mapping ''f'' from COSI ''U'' to COSI ''V'' is analyzed in terms of a mapping ''g'' that takes individuals to individuals, ignoring their inner structures, and a set of mappings ''h''_''j'', where ''j'' ranges over the individuals of COSI ''U'', and where ''h''_''j'' specifies just how the parts of ''j'' map to the parts of ''g''(''j''), its counterpart under ''g''.

The general scheme of things is suggested by the following Figure, where the mapping <math>f\!</math> from COSI <math>U\!</math> to COSI <math>V\!</math> is analyzed in terms of a mapping <math>g\!</math> that takes individuals to individuals, ignoring their inner structures, and a set of mappings <math>h_j,\!</math> where <math>j\!</math> ranges over the individuals of COSI <math>U,\!</math> and where <math>h_j\!</math> specifies just how the parts of <math>j\!</math> map to the parts of <math>g(j),\!</math> its counterpart under <math>g.\!</math>

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