Not quite. Chemical categories, for example, are real, actual identifiable consistent functions of the universe that happen in observable, consistent ways on the basis of fixed process.
Hydrogen isn't imaginary, it's a function of the universe!
Are you sure?
Is a proton hydrogen, or does it need an electron in order to be hydrogen?
A bare proton is ionized hydrogen.
If it doesn't need an electron, then how do protons in a helium nucleus stop also being hydrogen atoms?
Elements persist even in the absence of electrons. A nuclear physicist can identify elements in the heart of a white dwarf even though a chemist would have thrown up his hands and said "there is no chemistry here".
If it does need an electron, then what is metallic hydrogen doing? And how come a hydrogen ion isn't hydrogen, but a sodium ion is still sodium? Or is it?
I have heard of "ionized hydrogen" plenty of times.
Chemical elements are categories, and as such are an imaginary human construct, that we use to impose order on our thoughts about our world. They map fairly closely with a bunch of stuff that's apparently real, but that's not proof that (or even evidence that) they aren't imaginary, and even with an example like this, where the mapping between our imaginings and our reality is very close indeed, we can find discrepancies - places where the categorisation is not particularly helpful as a description of anything real.
The structure of the outer electron shell has a substantial effect on how they behave. Noble gases are clearly a category. Column 1 and column 17 are likewise pretty darn clear.
I guess my point still stands? Either way, there is not some fundamental principle of the universe that causes sex to fall into well defined categories for which there is a specific set of quantum, discrete states it can occupy.
Sex is unlike chemistry, insofar as there is no completion of the concept.
The periodic table is a complete and ostensibly infinite function of the configurations and stabilities of electron, proton, and neutrons and their shell behaviors and the way they are constrained by immutable laws of nature.
There is nothing immutable constraining sex in the same way. There are game theoretic principles around reproduction and diffusion of populations, but nothing is actually bound to follow them perfectly.
Electrons and protons cannot behave in ways outside of the available quantum states. It's not that they don't, they literally can't. The universe just will not let them. We've tried.
The universe will absolutely allow all kinds of variance on the topic of sex. It already does, from vastly polysexual organisms like some fungi and bacteria, to intersexed organisms, to asexual and non-reproductive individuals whose only role in a group is to support.
People act as if there is some fundamental ethical obligation to reproduce and to stay reproductive, but for fuck, sakes look at bees, or ants.
There's like 1-2 reproductive individuals among tens of thousands, or even millions.
Clearly the "every individual reproduces" paradigm is not naturally necessary.
Indeed people call female worker bees female, and yet... Well... Yes, they have ovipositors, but they don't actually have the capacity to create offspring.
We call them "female"... but are they? Then, maybe the scientific community DOESN'T call them female anymore, I haven't checked lately.
There is no periodicity, no hard requirement, that sex even exist as a concept among some class of organism.
It's hard to even call what fungi do "sex" either for that matter. Genetic material is distributed by fungi in a fundamentally different way than it is among other organisms, creating an environment where compatibility is more like a heuristic than the quasi-binary that other organisms have.
In software, one learns similarly that there are two families of types, of categorization.
There is a family of types hard categories, of instruction.
There is also a family of types only defined by usage and usefulness, too, though... Data types.
The problem is that 0x4EE7BEEF is not an "integer" or a "boolean" or a "float" the same way "human being" is not a "man" a "woman" or an "asshole"... Or even really "a human being".
We subjectively consider and treat it like such, play a little game where we pretend that these things have meaning, casting them because it helps us keep strait which math to use where to get the result we want, but by the time that they become instructions, that meaning has been completely stripped away, torn off and thrown out, in most compiled languages.
Indeed, "man" is like "int". It's not so much about the thing itself, but rather about how it behaves in the system.