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## Comments

1) The monogamous spousal function for all people, where unmarried people are treated as their own spouse.

The spouse, \(s\), of my spouse, \(z_1\) is me, \(z_0\).

2) The a mother, \(a\), of only children, \(c\), where \(g\) is the firstborn and \(h\) the last.

`1) The monogamous spousal function for all people, where unmarried people are treated as their own spouse. The spouse, \\(s\\), of my spouse, \\(z_1\\) is me, \\(z_0\\). 2) The a mother, \\(a\\), of only children, \\(c\\), where \\(g\\) is the firstborn and \\(h\\) the last.`

About 2 - it looks like the morphisms

gandhshould really be the same morphism, is there a way to show this? If we had a reverse morphism \(f^{-1}: b \to a\), such that \(f \cdot f^{-1} = id_b\) then this would follow naturally, but we don't. We just have some image ofa, \(f: a \to Im(a)\), inb. So basically we are saying that this equality holds only for a subset ofb, other entries may have different outcomes fromgandh.EDIT: got it, ifacontains mothers with a single child, andbis the set of all mothers, then \(f.g = f.h\), but in general, for other mothers, the first child and the last are not equal.`About 2 - it looks like the morphisms **g** and **h** should really be the same morphism, is there a way to show this? If we had a reverse morphism \\(f^{-1}: b \to a\\), such that \\(f \cdot f^{-1} = id_b\\) then this would follow naturally, but we don't. We just have some image of *a*, \\(f: a \to Im(a)\\), in *b*. So basically we are saying that this equality holds only for a subset of *b*, other entries may have different outcomes from **g** and **h**. **EDIT**: got it, if _a_ contains mothers with a single child, and _b_ is the set of all mothers, then \\(f.g = f.h\\), but in general, for other mothers, the first child and the last are not equal.`