Each task in the L4Re system has access to two resource spaces (three on IA32) which are maintained by the kernel.

These are the

object space,
memory space, and
IO-port space (only on IA32).

The entities addressed in each space are capabilities to objects, virtual memory pages, and IO ports. The addresses are unsigned integers and the largest valid address depends on which space is referenced, the hardware, and the configuration of the kernel. Although a program can access memory at byte granularity, from the kernel's point of view the address granularity in the memory space is not bytes but pages, as determined by the hardware. The address of a capability is also called its "capability slot".

Flexpages describe a range in any of the spaces that has a power-of-two length and is also aligned to this length. They additionally hold access rights information and further space specific information.

When a resource is present at some address in a task's corresponding resource space, then we say that resource is mapped to that task. For example, a capability to the task's main thread may be mapped to capability slot 5, or the first page of the code segment a thread executes is mapped to virtual memory page 12345. However, there need not be any resource mapped to an address.

Tasks can exchange resources through a process called "mapping" during IPC and using the L4::Task::map() method. The sending task specifies a send flexpage and the receiving task a receive flexpage. The resources mapped to the send flexpage will then be mapped to the receive flexpage by the kernel.

Memory mappings and IO port mappings are hierarchical: If a resource of such a type is subject of a map operation, the received mapping is a child mapping of the corresponding mapping in the sending task (parent mapping). The kernel usually respects the relationship between these two mappings (granting is an exception; see below): If rights of a parent mapping are revoked using L4::Task::unmap(), these rights are also removed from its child mappings. Also, if a mapping is completely removed (via L4::Task::unmap() or by mapping something else at its place), then also all child mappings are removed. In contrast, revoking rights of a child mapping leaves the rights of its parent mapping untouched.

The mapping of a resource can be performed as grant operation (see L4_MAP_ITEM_GRANT): Such an operation includes the removal of all involved mappings from the send flexpage (basically a move operation). While with a map operation without grant the mapping in the send flexpage remains the parent of all child mappings (including the new child mapping in the receive flexpage), a grant operation moves the mappings covered by the send flexpage to the corresponding addresses from the receive flexpage while leaving the parent/child relationship of the moved mappings with other mappings untouched.

During a map operation at most the access rights of the source mapping(s) can be transferred but no additional rights can be added. So only rights that are present in the source mapping and that are specified in the send item/flexpage are transferred. This also holds for grant mappings, however, rights revocation is not guaranteed to be applied to descendant mappings in case of grant.

There are cases where a grant operation is not or cannot be performed as requested; see L4_MAP_ITEM_GRANT for details.

Object capabilities are not hierarchical – they have no children. The result of the map operation on an object capability is a copy of that capability in the object space of the destination task.