I didn't find the post itself to be snobbish. I liked the tone and pacing, I think that your algebra makes for an interesting topic, and it was laudable for you to write about it.
What I dislike is the bait-and-switch, wherein the lede implies a digression on an math topic, then the bulk of the content is going over mundane Haskell code.
I don't care if Haskell coders want to get together and code golf their homomorphisms all day, but I find it exploitative to package that up as an excursion into algebra. As someone who's interested in math, but honestly couldn't care less about Haskell, these posts are all noise to me.
In case you missed the tags right under the title: "coding, math; algebra, haskell." I wouldn't call this a bait-and-switch. (I was happy enough to learn that graph join and graph union distribute, and that they satisfy a certain algebraic relation. Though I wouldn't have minded more math.)
Sometimes I find that code works as a clear notation for math. Maybe you just have something against Haskell, but all of this could have been written in any other modern language without too much effort, and I find Haskell to be more on the mathy end. (By the way, I can't tell if you're against Haskell or homomorphisms!)
And I think this really is an excursion into algebra, more on the general algebraic structures end of things. One might say that this describes an algebraic theory of graphs, where your matrix representation is a particular construction which satisfies the theory. The very end, the "Basic" type, feels quite a lot like reading a book on general algebraic structures.
I have some questions about this algebra, like how decompositions work, and maybe I'll think about them sometime.
What I dislike is the bait-and-switch, wherein the lede implies a digression on an math topic, then the bulk of the content is going over mundane Haskell code.
I don't care if Haskell coders want to get together and code golf their homomorphisms all day, but I find it exploitative to package that up as an excursion into algebra. As someone who's interested in math, but honestly couldn't care less about Haskell, these posts are all noise to me.