Closed MatthiasHu closed 2 years ago
Wait a second, every function that admits a retract is an embedding, right? So retractableIntoSet→isEmbedding
had an unnecessary isSet
assumption too...
No, I was wrong: for example, Unit -> S^1
admits a retract but is not an embedding.
This PR removes an unnecessary assumption from
injEmbedding
inCubical.Functions.Embedding
. The naive definition of injectivity,∀{w x} → f w ≡ f x → w ≡ x
, is already sufficient forf
to be an embedding ifB
is a set, we don't need thatA
is a set.I also deleted
retractableIntoSet→isEmbedding
, because it shows the same thing under the stronger assumption thatf
has a retract.