diff --git a/src/GAP/iso_gap_oscar.jl b/src/GAP/iso_gap_oscar.jl
index 237dda9a85fa..dcf81019c919 100644
--- a/src/GAP/iso_gap_oscar.jl
+++ b/src/GAP/iso_gap_oscar.jl
@@ -288,6 +288,14 @@ GAP: x_1^2+x_1+1
 julia> f(y) == pol
 true
 ```
+
+!!! warning
+    The functions `Oscar.iso_gap_oscar` and [`Oscar.iso_oscar_gap`](@ref)
+    are not injective.
+    Due to caching, it may happen that `S` stores an attribute value
+    of `Oscar.iso_oscar_gap(S)`,
+    but that the codomain of this map is not identical with
+    or even not equal to the given `R`.
 """
 iso_gap_oscar(F::GAP.GapObj) = GAP.Globals.IsoGapOscar(F)
 
@@ -309,8 +317,9 @@ push!(_iso_gap_oscar_methods, "IsRing and IsZmodnZObjNonprimeCollection" => _iso
 push!(_iso_gap_oscar_methods, "IsUnivariatePolynomialRing" => _iso_gap_oscar_univariate_polynomial_ring)
 push!(_iso_gap_oscar_methods, "IsPolynomialRing" => _iso_gap_oscar_multivariate_polynomial_ring)
 
-# Note that `IsNumberFieldByMatrices` is a property, but the alnuth package
-# uses it like a category, i.e., one can rely on the fact that
+# Note that `IsNumberFieldByMatrices` is a GAP property,
+# but the alnuth package uses it like a GAP category,
+# i.e., one can rely on the fact that
 # this filter is set in a field generated by matrices .
 push!(_iso_gap_oscar_methods, "IsField and IsNumberFieldByMatrices" => _iso_gap_oscar_number_field)
 
diff --git a/src/GAP/iso_oscar_gap.jl b/src/GAP/iso_oscar_gap.jl
index 1377b5b55a52..4ebd119db083 100644
--- a/src/GAP/iso_oscar_gap.jl
+++ b/src/GAP/iso_oscar_gap.jl
@@ -382,6 +382,14 @@ GAP: x_1^2+x_1-1
 julia> preimage(f, y) == pol
 true
 ```
+
+!!! warning
+    The functions `Oscar.iso_oscar_gap` and [`Oscar.iso_gap_oscar`](@ref)
+    are not injective.
+    Due to caching, it may happen that `S` stores an attribute value
+    of `Oscar.iso_gap_oscar(S)`,
+    but that the codomain of this map is not identical with
+    or even not equal to the given `R`.
 """
 @attr Map function iso_oscar_gap(F)
    return _iso_oscar_gap(F)
@@ -411,7 +419,7 @@ function _iso_oscar_gap_polynomial_ring_functions(RO::PolyRing{T}, RG::GAP.GapOb
    return (f, finv)
 end
 
-function _iso_oscar_gap(RO::PolyRing{T}) where T
+function _iso_oscar_gap(RO::PolyRing)
    coeffs_iso = iso_oscar_gap(base_ring(RO))
    RG = GAPWrap.PolynomialRing(codomain(coeffs_iso))