somniloquism

A map f: {article, preposition} -> {word}, telling that both ‘article’ and ‘preposition’ are words, factored through an object {of, the} into the composite of a map h: {of, the} -> {word}, telling both ‘of’ and ‘the’ are words, after another map g: {article, preposition} -> {of, the} adding that ‘the’ is an example of article and ‘of’ that of preposition (Conceptual Mathematics, pp. 84-5).

Since there is more than the ‘to the or not to a‘ that we are trying to understand, we say

f: A -> B, A = {a1, a2}, B = {b}

g: A -> C, h: C -> B, C = {c1, c2}

and call it a day

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