Proposed resolution:

This wording is relative to N4917.

1. Modify [iterator.traits] as indicated:

   -2- The definitions in this subclause make use of the following exposition-only concepts:

   […]
   template<class I>
   concept cpp17-forward-iterator =
     cpp17-input-iterator<I> && constructible_from<I> &&
     is_lvalue_reference_v<iter_reference_t<I>> &&
     same_as<remove_cvref_t<iter_reference_t<I>>,
             typename indirectly_readable_traits<I>::value_type> &&
     requires(I i) {
       {  i++ } -> convertible_to<const I&>;
       { *i++ } -> same_as<iter_reference_t<I>>;
     };
   […]
   

2. Modify [range.transform.iterator] as indicated:

   -2- The member typedef-name iterator_category is defined if and only if Base models forward_range. In that case, iterator::iterator_category is defined as follows: Let C denote the type iterator_traits<iterator_t<Base>>::iterator_category.

   1. (2.1) — If is_lvalue_reference_v<invoke_result_t<maybe-const<Const, F>&, range_reference_t<Base>>> is true, then

      1. (2.1.1) — if C models derived_from<contiguous_iterator_tag>, iterator_category denotes random_access_iterator_tag;

      2. (2.1.2) — otherwise, iterator_category denotes C.

   2. (2.2) — Otherwise, iterator_category denotes input_iterator_tag.

3. Modify [range.join.with.iterator] as indicated:

   -2- The member typedef-name iterator_category is defined if and only if ref-is-glvalue is true, and Base and InnerBase each model forward_range. In that case, iterator::iterator_category is defined as follows:

   1. (2.1) — […]

   2. (2.2) — If

      is_lvalue_reference_v<common_reference_t<iter_reference_t<InnerIter>,
                            iter_reference_t<PatternIter>>>
      

      is false, iterator_category denotes input_iterator_tag.

   3. (2.3) — […]

4. Modify [range.zip.transform.iterator] as indicated:

   -1- The member typedef-name iterator::iterator_category is defined if and only if Base models forward_range. In that case, iterator::iterator_category is defined as follows:

   1. (1.1) — If

      invoke_result_t<maybe-const<Const, F>&, range_reference_t<maybe-const<Const, Views>>...>
      

      is not an lvalue reference, iterator_category denotes input_iterator_tag.

   2. (1.2) — […]

5. Modify [range.adjacent.transform.iterator] as indicated:

   -1- The member typedef-name iterator::iterator_category is defined as follows:

   1. (1.1) — If invoke_result_t<maybe-const<Const, F>&, REPEAT(range_reference_t<Base>, N)...> is not an lvalue reference, iterator_category denotes input_iterator_tag.

   2. (1.2) — […]