Open jamesmckinna opened 8 months ago
The binary product of Setoid
s is in Data.Product.Relation.Binary.Pointwise.NonDependent
: https://agda.github.io/agda-stdlib/master/Data.Product.Relation.Binary.Pointwise.NonDependent.html#7308. I don't know if we already have currying defined for setoids of the top of my head.
Thanks @Taneb ! I'd just about managed to find that for myself while working on #2348 / #2350 but... not the first place I might have looked for it!
A known, thorny issue: finding things in stdlib is very hard.
As I said on #2348 : it makes sense for the constructions to be in Construct
but the definitions of the structure shouldn't be in the same place.
Will Wreath
be a construction (only) or will it need new structures? I don't have a strong opinion on Wreath
vs SemiDirect
.
Well, again, all good questions!
I think that as a construction, I should at least also need Algebra.Construct.Pointwise
which does not at present exist, AFAICT. (And that is a construction... not a definition).
As for WreathProduct itself, I think that that is also a construction: given a monoid, a monoid action, then ... such and such setoid ... also admits a monoid structure...
Good, I think this is converging to a design: indeed WreathProduct
is a construction and so Construct
is a great home for it. Yes, having a pointwise product construction would also be good. Whoever needs it first can build it.
And yes: Construct.Pointwise
(properly, should we say: Power
and Copower
?) should, in turn, be factored out as a distinct issue/PR!
UPDATED: #2381
This fell originally under #2348 but I think should be factored out on its own.
Current issues:
Setoid
s defined? (plus currying etc.: cartesian-closedness ofSetoid
?)Setoid
to an algebraic structure/bundle defined, and its properties established?Wreath
(my preferred target) orSemiDirect
?Monoid
with aMonoidAction
(#2348 / #2350 ), but many kinds of variants exist according to how much structure is present. How/where to accommodate them all?Re: the last point. previously I wrote on #2348 as follows: (This, viz. adding wreath products, as an instance of combining 'things-acted-upon-by-things') "... is complicated by the plethora of various definitions in the literature (according to the 'thinginess' involved), and the relationship with 'semi-direct product's... so perhaps some discussion/downstream refactoring may be necessary. "