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Can (B, f) where f : A -> B for some f, A, B be safely considered an F-Algebra for Const A?

(B, f)

f : A -> B

f, A, B

Const A

yup

Is it good idea to think of F-Algebra morphisms as morphisms that go from object with "more structure" to object with "same/less structure"? As in, their laws couldn't hold if I went from "less" to "more structure", could they?

Can

`(B, f)`

where`f : A -> B`

for some`f, A, B`

be safely considered an F-Algebra for`Const A`

?yup

Is it good idea to think of F-Algebra morphisms as morphisms that go from object with "more structure" to object with "same/less structure"? As in, their laws couldn't hold if I went from "less" to "more structure", could they?