Closed zickgraf closed 1 year ago
I have seen on nLab that
IsDistributiveCategory
is standard terminology for a bicartesian category with a distributivity law for products and coproducts. I would still suggest to call itIsDistributiveBicartesianCategory
in CAP to avoid confusion, especially if we later introduceIsDistributiveMonoidalCategory
. Otherwise it would be very easy to confuseIsMonoidalCategory and IsDistributiveCategory
andIsDistributiveMonoidalCategory
, i.e. assume an implication in at least one direction.
IsDistributiveMonoidalCategory
only makes sense if we know over what the tensor product distributes. In case of the direct sum we already call it "additive monoidal categories". However, we did not introduce the corresponding and-filter.
IsDistributiveMonoidalCategory
only makes sense if we know over what the tensor product distributes.
nLab says: "A distributive monoidal category is a monoidal category whose tensor product distributes over coproducts." But indeed it also mentions that "this is not entirely standard terminology".
In case of the direct sum we already call it "additive monoidal categories". However, we did not introduce the corresponding and-filter.
Which and-filter do you mean?
In case of the direct sum we already call it "additive monoidal categories". However, we did not introduce the corresponding and-filter.
Which and-filter do you mean?
IsAdditiveMonoidalCategory
. I believe we did not introduce it since a monoidal structure on an additive category does not necessarily distribute over the direct sum. E.g., the direct sum as a monoidal structure does not distribute over itself.
The terminology IsDistributiveMonodialCategory
on nLab is biased towards coproduct.
I still find IsDistributiveCategory
confusing (independent of the existence and/or definition of IsDistributiveMonodialCategory
) and would suggest naming it IsDistributiveBicartesianCategory
. However, if you think IsDistributiveCategory
is generally understood, feel free to close the issue.
What about making IsDistributiveBicartesianCategory
a synonym? We can wait until Julia supports DeclareSynonym
.
Would IsDistributiveBicartesianCategory
be a synonym of IsDistributiveCategory
or the other way round? I.e. would Display( IsDistributiveBicartesianCategory )
print
<Property "IsDistributiveCategory">
or
<Property "IsDistributiveBicartesianCategory">
?
Display( IsDistributiveBicartesianCategory )
would print IsDistributiveCategory
.
Display( IsDistributiveBicartesianCategory )
would printIsDistributiveCategory
.
I think this would be even more confusing :D I will close the issue.
I have seen on nLab that
IsDistributiveCategory
is standard terminology for a bicartesian category with a distributivity law for products and coproducts. I would still suggest to call itIsDistributiveBicartesianCategory
in CAP to avoid confusion ~, especially if we later introduceIsDistributiveMonoidalCategory
. Otherwise it would be very easy to confuseIsMonoidalCategory and IsDistributiveCategory
andIsDistributiveMonoidalCategory
, i.e. assume an implication in at least one direction~.