Blake Shaw schreef op wo 15-06-2022 om 21:40 [+0000]:
> On the contrary, lets say I'm writing an intro book on CT. If I'm
> demonstrating something trivial, say the initial object, I'm not
> going to refer to it as "an initial-like object" for the sake of
> generality.

Neither does Guix?  If you're in a context where only the basic object
(in this case, your demonstration the initial object) is used, just
talk about the basic object.  But in a later section where you
generalize things to ‘initial-like objects’ (whatever that would be in
CT, I don't know any CT), you talk about ‘initial-like objects’, not
‘initial object and initial-like objects’.

For an example from another domain, consider groups in algebra.
In group theory, we have e.g. the fundamental theorem on homomorphisms.
Wikipedia formulates this as:

Given two groups G and H and a group homomorphism f : G → H, let K be a
normal subgroup in G and φ the natural surjective homomorphism G → G/K
(where G/K is the quotient group of G by K). If K is a subset of ker(f)
then there exists a unique homomorphism h: G/K → H such that f = h∘φ.

An equivalent statement could be made by replacing ‘given a group’ by
‘given an Abelian group or a group’:

Given two Abelian groups or groups G and H and a group homomorphism f :
G → H, let K be an Abelian normal subgroup or normal subgroup in G and
φ the natural surjective homomorphism G → G/K (where G/K is the
quotient group of G by K). If K is a subset of ker(f) then there exists
a unique homomorphism h: G/K → H such that f = h∘φ.’

But why do such a pointless thing, wouldn't just talking about groups
instead of ‘Abelian groups or groups’ be much simpler?

TBC: here ‘file-like object’ ≃ ‘group’ and ‘file’ = ‘Abelian group’.

Greetings,
Maxime.