In his study of the Yawalapíti cosmology (see The Inconstancy of the Indian Soul, chapter 1), Eduardo Viveiros de Castro describes spirits (specters), animals and humans as being perspectives. They are different ways in which things can be seen and recognized. They are not fixed, one can have different perspectives depending on the body one finds oneself in a circumstance, on the surroundings one is - whether in the forest or outside it because in the forest one is easily an animal and sometimes a spirit - and on the degree of shamanic intensity one is on. They are not a substantive taxonomy, they are indexicals. Further, he writes that from the point of view of spirits, humans and animals are alike while from the point of view of humans there are similarities between animals and spirits and finally from the point of view of animals, humans and spirit are perhaps the same.
Now, a cosmopolitical moment is like a cosmic epoch with its goals, its fears, its defenses, its dreams and its nightmares. Take the age of nihilism (the age of metaphysics). It fosters technology, science, the controlability of the world, Machenschaft (Heidegger's word), the world being put in a standing reserve etc because it is guided by the goal of dealing with anything else in terms of an extraction of its intelligibility. It is the age of intelligence, perhaps of a certain intelligence, of a strong commanding intelligence. That age has its defenses: religion as a mode of making cosmology into a discourse of salvation for salvation is on the agenda since everything can be turned into a controllable tool for a predating Wille zu Macht. It has nightmares too: a world of contingency and chaos is one of them - a world where nothing can be controlled. Concerning a cosmopolitical age, humans are perhaps the stage where things happen, but not the protagonists - they can cause change without intending or, rather, the fate of the age is not pending on a human decision and yet is not fully imposed on humans.
The approach to cosmopolitics I would favor would bring together what Descola calls dispositions concerning nature (or the nonhuman), what Stengers calls an ecosystem of practices and what Heidegger means with a history of Beyng. According to the three of them, nihilism is a cosmopolitical event - an event in the history of Beyng, an ecological arrangement of practices and a (naturalist) disposition towards what is not human. In all three approaches, it is connected to the age of capital which is a cosmic epoch in its own right.
Capital has its goals - melting, abstracting work, forging the commodification of the world -, its fears - a general uprise against its power -, its defenses - fascism being the most salient one -, its dreams - a world where excess is itself money - and its nightmares - any form of commons (or communisms). It has to keep this things up in order to carry on - it lives while it attends to these features. Humans are also the stage where the history of capital takes place and its destruction is neither a decision humans can sovereignly have nor an imposition on them - it involves preparation for an appropriate transforming event. Perhaps cosmopolitical ages are like Tim Morton's hyperobjects with great extensions and long durations. They certainly involve the future as much as the past and the present; they are temporal hyperobjects. But I would like to propose a different approach.
Perhaps cosmopolitical ages are like animals. They are incarnations that affect everything else - they act somehow like nature, like the body where any deliberation acts upon. If we see them as animals, we see them independently of any macropolitical choice - they are the ground on which these choices are made. The idea then is that cosmopolitical ages are like animals, macropolitical ages are like humans (they are often too grounded on the human scale anyway) and micropolitical ages are like spirit - they are about dealing with the other that is in front of us, in a face-to-face basis.
There it is: three perspectives, a cosmopolitical one, a macropolitical one and a micropolitical one. A regime of a otherness that determines the grammar of the encounter - the body and skin of the animals -, a macropolitical order that rules the human community and takes humans and nonhumans as ingredients in its concotions and a micropolitical spirit that is the encounter itself, the very moment where something appears in front of us. The three together compose a kind of (Yawalapíti) xenoghraphy. Each event can be seen in these three different perspectives and each encounter can be seen as meeting an animal, a human or a spirit. The event is what comes, what comes in our direction, Ereignis, arrival, happening.