> Matthew, you keep editing your comments when people comment on them. This makes it difficult to make sense of other people's comments. It also makes it hard to follow the conversation and see how it is developing.

Okay, so in the future if I make a mistake in terms of a proof or some jargon, what should I do? Would you prefer I left my old post intact, and then make a new post with the corrections?

I can't help making mistakes. I would strongly prefer to correct them as I learn.

> Let me make a further comment. You introduce some seemingly new jargon "upper semilattice" but don't tell us what it is, instead you link to a random part of a wikipedia page. Be explicit, tell us what this means, otherwise herein lies a good place for errors to creep in. Similarly tell us why you need this new jargon. There's a danger of mixing terminology from different areas, namely category theory type monoidal preorder language and lattice theory in that they are based on different perspectives, although they might be equivalent, there's plenty of scope for confusing things. It's fine to say a monoidal preorder with a widget is the same as sprocket semi-lattice or something if that helps clarify, but usually you would need to prove such a thing.

Okay, I was talking about a semilattice with arbitrary joins, and I thought I linked to the relevant wikipedia page. I am sorry for not motivating this or complete-rigs. It looks like it's just you, me, Keith, and Anindya in this this thread, so I thought I could get away without motivating these things.

I don't always know the name of some mathematical object. I like making definitions and reasoning about them. Should I use a convention like this?

> **Invented Definition** An object \\(\Omega\\) is an *ultra-fibered ideal* if and only if...