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I really like this, but one change I'd like to see: given how many structures are defined in terms of simpler structures (which are defined in terms of yet simp

I really like this, but one change I'd like to see: given how many structures are defined in terms of simpler structures (which are defined in terms of yet simpler ones), it would be nice if a structure listed all of the laws, not just the ones that simpler structures don't. That way, you would have to jump around the page to get a complete picture of a single structure. Maybe have them be a different color, so you can see what is new vs. what is inherited?

joker3 7y ago
It's somewhat confusing to see it this way the first time, but it's absolutely the right way to think about these structures. It's better to do the work to get used to it early on.
- mcphage 7y ago
  It's the right way to think about the structures, sure. But when you want to look up the laws for what makes something a Ring, for instance, having them all in 1 place instead of having to jump between: Monoid, Semigroup, Group, Abelian Group, Quasiring, Nearring, and Ring. (And some of those laws occur twice, for different operators) makes it a lot more useful as a reference document.
  - BoiledCabbage 7y ago
    That's like saying when implementing a function you shouldn't call another fn, you should copy and paste its implementation so you don't have to flip to another location in the code. The right way is to learn what the function means so you can set see calls to it and know what it does.
    - mcphage 7y ago
      The purpose of the site is to be: > So, that’s the intent of this post – to be that fast reference to the kinds of algebraic structures I care about. I learned these structures in the early 90s; I don’t need to be told the right way to learn them. However, a “fast reference” would be useful.
      - srean 7y ago
        For arithmetic properties and definitions do you suggest tracing them right to Peano axioms ?
        mcphage 7y ago
        If the page had arithmetic structures, then obviously yes. Groups don’t include those properties, which is why they are not listed, and that is a very important distinction.

joker3 7y ago

It's somewhat confusing to see it this way the first time, but it's absolutely the right way to think about these structures. It's better to do the work to get used to it early on.

mcphage 7y ago
It's the right way to think about the structures, sure. But when you want to look up the laws for what makes something a Ring, for instance, having them all in 1 place instead of having to jump between: Monoid, Semigroup, Group, Abelian Group, Quasiring, Nearring, and Ring. (And some of those laws occur twice, for different operators) makes it a lot more useful as a reference document.
- BoiledCabbage 7y ago
  That's like saying when implementing a function you shouldn't call another fn, you should copy and paste its implementation so you don't have to flip to another location in the code. The right way is to learn what the function means so you can set see calls to it and know what it does.
  - mcphage 7y ago
    The purpose of the site is to be: > So, that’s the intent of this post – to be that fast reference to the kinds of algebraic structures I care about. I learned these structures in the early 90s; I don’t need to be told the right way to learn them. However, a “fast reference” would be useful.
    - srean 7y ago
      For arithmetic properties and definitions do you suggest tracing them right to Peano axioms ?
      - mcphage 7y ago
        If the page had arithmetic structures, then obviously yes. Groups don’t include those properties, which is why they are not listed, and that is a very important distinction.