🔬 Calcium triggers natural transformation in 𝐴𝑐𝑖𝑛𝑒𝑡𝑜𝑏𝑎𝑐𝑡𝑒𝑟 𝑏𝑎𝑢𝑚𝑎𝑛𝑛𝑖𝑖, boosting DNA uptake and resistance acquisition, reports the Charpentier Lab. Opens new doors for genetic engineering.

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I've got a "higher-order" hylomorphism (of type `{k : Type} -> {f : (k -> Type) -> k -> Type} -> HFunctor f -> {i, o : k -> Type} -> Coalgebra f i -> Algebra f o -> NaturalTransformation i o`.

I'd like to generalize this in the same way that `ghylo` generalizes `hylo` / `refold`, but I'm not […]

Sometimes it annoys me that (k -> Type) -> k -> Type and (k -> Type, k) -> Type aren't the same.

hfreeWrap : {f : (k -> Type) -> k -> Type} -> {a : k -> Type} -> NaturalTransformation (f (HFree f a)) (HFree f a)

Should be able to be written as

hfreeWrap : {f : (k -> Type) -> k -> Type) -> […]

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We propose a model where calcium acts as a signal triggering natural transformation through both transcriptional regulation and structural activation of the type IV pilus.
#naturaltransformation #typeivpilus

And with this #idris :

```
hchrono : {k : Type} -> {f : (k -> Type) -> k -> Type} -> HFunctor f
-> {i, o : k -> Type}
-> Coalgebra (f . HFree f) i -> Algebra (f . HCofree f) o
-> NaturalTransformation i o
hchrono hmap =
ghhylo
{f} hmap
(hmonadHfree {f} hmap) (hcomonadHcofree {f} hmap) […]

Tonight's Idris work ends with no build error, but "just" with 4 holes unfilled:

```
hchrono : {k : Type} -> {f : (k -> Type) -> k -> Type} -> HFunctor f
-> {i, o : k -> Type}
-> Coalgebra (f . HFree f) i -> Algebra (f . HCofree f) o
-> NaturalTransformation i o
hchrono hmap c a = ghhylo hmap […]

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