How to create STL map of set where set uses a comparator

My issue is simple, I want to have a map of set where the set uses lambda comparator

auto comp = [](const int& i, const int& j) {
    return i < j;
};

map<int, set<int>> map1;
map<int, set<int, decltype(comp)>> map2;

set<int, decltype(comp)> set1(comp);      // works fine
map1[0] = set<int>();                     // works fine
map2[0] = set<int, decltype(comp)>(comp); // compile error

There is some syntax which is wrong which I don't know nor I could find any resource on web which is doing what I want to do

The compiler error is a very long message which I pasted below for the complete picture.

In file included from a.cpp:1:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/set:458:19: error: no matching constructor for initialization of 'std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >::value_compare' (aka '(lambda at a.cpp:8:17)')
        : __tree_(value_compare()) {}
                  ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/tuple:1360:7: note: in instantiation of member function 'std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >::set' requested here
      second(_VSTD::forward<_Args2>(_VSTD::get<_I2>(__second_args))...)
      ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/utility:509:11: note: in instantiation of function template specialization 'std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >::pair<int &&, 0>' requested here
        : pair(__pc, __first_args, __second_args,
          ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:1825:31: note: in instantiation of function template specialization 'std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >::pair<int &&>' requested here
            ::new((void*)__p) _Up(_VSTD::forward<_Args>(__args)...);
                              ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:1717:18: note: in instantiation of function template specialization 'std::__1::allocator<std::__1::__tree_node<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, void *> >::construct<std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, const std::__1::piecewise_construct_t &, std::__1::tuple<int &&>, std::__1::tuple<> >' requested here
            {__a.construct(__p, _VSTD::forward<_Args>(__args)...);}
                 ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:1560:14: note: in instantiation of function template specialization 'std::__1::allocator_traits<std::__1::allocator<std::__1::__tree_node<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, void *> > >::__construct<std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, const std::__1::piecewise_construct_t &, std::__1::tuple<int &&>, std::__1::tuple<> >' requested here
            {__construct(__has_construct<allocator_type, _Tp*, _Args...>(),
             ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/__tree:2202:20: note: in instantiation of function template specialization 'std::__1::allocator_traits<std::__1::allocator<std::__1::__tree_node<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, void *> > >::construct<std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, const std::__1::piecewise_construct_t &, std::__1::tuple<int &&>, std::__1::tuple<> >' requested here
    __node_traits::construct(__na, _NodeTypes::__get_ptr(__h->__value_), _VSTD::forward<_Args>(__args)...);
                   ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/__tree:2147:29: note: in instantiation of function template specialization 'std::__1::__tree<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, std::__1::__map_value_compare<int, std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, std::__1::less<int>, true>, std::__1::allocator<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > > > >::__construct_node<const std::__1::piecewise_construct_t &, std::__1::tuple<int &&>, std::__1::tuple<> >' requested here
        __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
                            ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/map:1431:20: note: in instantiation of function template specialization 'std::__1::__tree<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, std::__1::__map_value_compare<int, std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > >, std::__1::less<int>, true>, std::__1::allocator<std::__1::__value_type<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > > > >::__emplace_unique_key_args<int, const std::__1::piecewise_construct_t &, std::__1::tuple<int &&>, std::__1::tuple<> >' requested here
    return __tree_.__emplace_unique_key_args(__k,
                   ^
a.cpp:17:9: note: in instantiation of member function 'std::__1::map<int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >, std::__1::less<int>, std::__1::allocator<std::__1::pair<const int, std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> > > > >::operator[]' requested here
    map2[0] = set<int, decltype(comp)>(comp);
        ^
a.cpp:8:17: note: candidate constructor (the implicit copy constructor) not viable: requires 1 argument, but 0 were provided
    auto comp = [](const int& i, const int& j) {
                ^
a.cpp:8:17: note: candidate constructor (the implicit move constructor) not viable: requires 1 argument, but 0 were provided
In file included from a.cpp:1:
In file included from /Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/set:402:
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/__tree:1752:14: error: object of type 'std::__1::__compressed_pair<unsigned long, (lambda at a.cpp:8:17)>' cannot be assigned because its copy assignment operator is implicitly deleted
    __pair3_ = _VSTD::move(__t.__pair3_);
             ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/__tree:1819:5: note: in instantiation of member function 'std::__1::__tree<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >::__move_assign' requested here
    __move_assign(__t, integral_constant<bool,
    ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/set:562:21: note: in instantiation of member function 'std::__1::__tree<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >::operator=' requested here
            __tree_ = _VSTD::move(__s.__tree_);
                    ^
a.cpp:17:13: note: in instantiation of member function 'std::__1::set<int, (lambda at a.cpp:8:17), std::__1::allocator<int> >::operator=' requested here
    map2[0] = set<int, decltype(comp)>(comp);
            ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:2208:27: note: copy assignment operator of '__compressed_pair<unsigned long, (lambda at a.cpp:8:17)>' is implicitly deleted because base class '__compressed_pair_elem<(lambda at a.cpp:8:17), 1>' has a deleted copy assignment operator
                          private __compressed_pair_elem<_T2, 1> {
                          ^
/Applications/Xcode.app/Contents/Developer/Toolchains/XcodeDefault.xctoolchain/usr/include/c++/v1/memory:2169:50: note: copy assignment operator of '__compressed_pair_elem<(lambda at a.cpp:8:17), 1, true>' is implicitly deleted because base class '(lambda at a.cpp:8:17)' has a deleted copy assignment operator
struct __compressed_pair_elem<_Tp, _Idx, true> : private _Tp {
                                                 ^
a.cpp:8:17: note: lambda expression begins here
    auto comp = [](const int& i, const int& j) {
                ^
2 errors generated.