Well, as I said I will explain a little more about the abstract beings in Digimon. The lore regarding this has been started thanks to the ideas established in Digimon Adventure that were then continued again in other works of the franchise.
Initially there existed a primordial world known as Idea, a chaotic world without order where there were souls and a souless being (Demiurge). In this world there were also the Ideas / Concepts, each one being an abstraction. These concepts formed laws, in that the world in its beginning had no order and the concepts fought each other.
Then in a moment the Order began, which divided the Ideas of Idea into two sides, and would establish what would be the concepts that would give the laws on these two sides.
The two sides would be known as "World of Light" and "World of Darkness". The totality of these worlds would be included in the opposing concepts of Light and Darkness. Light represents life and evolution. But darkness represents death and no-evolution.
Within the Light (Evolution) there are several positive concepts that are part of it, is what we see in Adventure as being Courage, Friendship, Knowledge, etc.
While within the Darkness there are negative concepts, bad thoughts like sins, the malice that exists within the hearts of all.
As you talked about elements, these concepts are related to some elements. At the time of creation of the Digital World (which is one of the parts that make up the World of Light) some materials were made using the concepts that exist within evolution, these concepts would then be related to some elemental power. For example, Courage is related to Fire, Friendship with Lightning, etc.
There are some beings that are born of these concepts, the Fire that represents the Firewall for example gave origin to Meramon and Birdramon. There are still beings who are most directly direct manifestations of these concepts, such as Agnimon who is a incarnation of Firewall.
To better explain the Firewall (also called the Wall of Fire in Digimon Adventure) is what divides the World of Light and the World of Darkness, has the function of not letting the worlds connect and tries to nullify any kind of interaction between them . However with the passage of time sometimes there are gaps in the Firewall, which allow a more direct connection between the two worlds.
Now that I've explained some of the context for concepts, then it's time to give examples.
Yggdrasil is possibly the greatest, it is the Order itself that put an end to chaos. It was It who established the laws that would govern the world.
It is also good to mention Homeostasis, it is not really an abstract being, but rather an agent of the Order. It exists as a being close to the level of the abstract trying to maintain the balance of Light and Darkness that existed since the beginning of time. When the balance balance tries to one side, Homeostasis acts to recover the universal balance.
The Seven Great Demon Lords are the manifestation of the Seven Deadly Sins. The biggest of them is Lucemon, which is actually the total manifestation of the concept of Darkness.
Although there are other interactions of the concepts, Apocalymon is one of them. Apocalymon is another interpretation of the Concept of Darkness, being strengthened thanks to all that leave the light. The goal of Apocalymon is to destroy the World of Light by expanding the infinite World of Darkness so that all may deify the darkness.
Bolt Boultamon is a "new" idea of Darkness, it had its origin still as part of the original Darkness, however it managed to separate from the past and became a concept of its own. Being a new concept of darkness Bolt Boutamon not only wishes to destroy the World of Light, but also to destroy the World of Darkness to start a new world.
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All in all we know more of beings that are not really concepts, but act in the name of these concepts. The Great Angels, for example, are beings who have received an aspect of God (Who was before with Lucemon) becoming the greatest of the angels. Ofanimon is responsible for caring for Love, while Cherubimon is responsible for keeping the Knowledge and Seraphimon is responsible for keeping all laws from occurring. There are still others like Mastemon, Raguelmon, and Rasielmon, but it is not known precisely what aspects of God they have received.
Beings like the Dark Masters are agents of Darkness, they receive power from the darkness and aim, even if unconsciously, to make it invade and nullify the light.Beings like the Dark Masters are agents of Darkness, they receive power from the darkness and aim, even if unconsciously, to make it invade and nullify the light.
The Four Holy Beasts are agents of the Light, they maintain the balance between the worlds acting as a force that keeps them in balance. When their power weakens the worlds they go into imbalance and run the risk of every thing to colliding, collapsing everything into darkness.
There are still those who exist as a subproduct of some concept, such as Mephismon which is a byproduct of Apocalymon, being a minor manifestation of the Idea of darkness.
There are also beings that are more connected to a concept. In this case the concept plays an essential part in their lives. These beings can be both human and Digmon, and when a Human and Digimon has a connection to the same concept, they can become Partners who draw power through these concepts more efficiently. In Digimon Adventure for example, Homeostasis chose the partners of the protagonists so that both are compatible with their main concepts.
There is still a case that has not yet been decided for sure, Death-X-mon. It is a being that is said to be death itself, but some say that this is just an exaggeration.
The concepts basically matter to Idea and the Physical World (a world created by Demiurge that exists as a shadow of Idea), but there are still worlds that exist beyond Idea and are not affected by concepts. One of these is the World of Eaters that exists beyond Idea, a world that exists beyond concepts and is completely incomprehensible. Yet even this world is but a tiny piece of an even larger system of higher worlds, referred to as the Work of God.
It is important to mention that God (or Gods) who created this system are not the same God that I referred to earlier. The God that I mentioned is said to be Yggdrasil, the very system that rules the entire Digital World.
I must say that I love the cosmology of Digimon, there is more to be said, but I do not know if you guys would like to read.