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Names and definitions in the +-IsAbelianGroup
instance of IsRing
#2247
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I agree that I also agree that doing the obvious conservative extension of defining subtraction is worthwhile. People can always choose to redefine and/or hide it if they have a more efficient version for their own instance. |
Question (perhaps for the |
The relationship is non-trivial because IsGroupoid is mostly about Whether this means that StrictGroupoid is the better thing to look at (I doubt it) or 0-Groupoids (most likely) is probably the right question to ask. |
OK, thanks for the steer towards a more refined analysis/understanding. I'm not about to propose adding |
Of the three points raised here, happy to close this with a successful merge of #2251 ... |
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Hi Three
Twoissues arising around(Is)Ring
(and friends):zero
inIsRing
#2195 do we really want the namesin the
+-IsAbelianGroup
instance ofIsRing
. Why not more simply+-inverse
etc.?Originally posted by @jamesmckinna in #2195 (comment)
UPDATED: so far, the use of these things is almost completely confined to 'internal' definitions in
Algebra.{Module.}Structures
andAlgebra.{Module.}Construct
, so I'll leave well alone for now...IsAbelianGroup
with an explicit subtraction operator?UPDATED: this already happens in
IsGroup
, though I might have expected theGroup
operation to admit two forms, and only collapse to 'subtraction' in theIsAbelianGroup
case... (?):UPDATED though if I were to, I'd define, in
IsGroup
see #2251 (and UPDATED to reflect the discussion there):and rename the first into
_-_
inIsAbelianGroup
and prove the two operations extensionally equal inAlgebra.Properties.AbelianGroup
(or somewhere else?)). Not sure about theinfix
/associativity declarations, though!Tempting instead, perhaps though, to define the Mal'cev operation and specialise it appropriately...
trans (sym ...) ...
analogous operation (not defined anywhere, AFAIK?) for theIsEquivalence
(Is)Groupoid
operations (with(Is)Groupoid
not defined anywhere, either AFAIK?) cf. Add derived (pre-)groupoid operations toRelation.Binary.Is(Partial)Equivalence
#2249The text was updated successfully, but these errors were encountered: