If Category Cuts has a single guiding claim, it is this: objects are not ontologically primary. They are outcomes—stabilisations produced by cuts within a relational field of possibility. What comes first are not things, but structures of potential instantiation.
This post makes that claim precise.
The Mistake of Beginning with Objects
Most ontologies begin by asking what exists. They inventory entities, then struggle to explain how those entities relate, change, or generate meaning. Even when relations are acknowledged, they are typically treated as secondary: links between already-constituted things.
Relational ontology inverts this order.
What we encounter, first, is not an object but a cut: a perspectival structuring of potential that yields an instance. Objects appear only after this cut, as relatively stable patterns within a wider field of possible patterns.
To ask “what is this?” is already to have performed a cut.
Categories as Theories, Not Collections
Category theory becomes relevant here not because it is abstract, but because it refuses to start with objects in the usual sense. A category is not a bag of things. It is a structure of relations governed by composability.
From a relational-ontological perspective, a category can be understood as:
a theory of possible instances, defined by what can meaningfully relate and compose within a given perspectival frame.
The so-called “objects” of a category are not substances. They are positions within a relational structure, defined entirely by the morphisms that connect them.
Instantiation Without Temporal Becoming
It is important to be precise here. When we speak of instantiation, we are not referring to a temporal process whereby something gradually comes into being. Instantiation is a perspectival event: the taking-up of a system as an instance.
A category, understood relationally, does not sit “behind” its instances as a hidden structure. Nor do instances exhaust it. Each instantiation is a cut that:
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actualises some relations,
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leaves others latent,
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and reshapes the horizon of further possible cuts.
Thus, a category is neither abstract nor concrete in the traditional sense. It is ontologically prior to that distinction.
Why Relations Must Come First
If we begin with objects, relations always appear contingent: something added after the fact. But if we begin with relations—with patterns of possible transformation—objects emerge as temporary stabilisations.
This is why morphisms, not objects, carry the real ontological weight.
A morphism is not a movement of something from A to B. It is a constraint on how cuts may compose. To say that two morphisms compose is to say that a particular sequence of perspectives is coherent within a given system.
Composition, then, is not a technical detail. It is the formal expression of relational intelligibility.
Failure as Ontological Signal
One of the most important consequences of this view is that failure of composition is informative.
When two cuts do not compose, this is not an error. It reveals something about:
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the limits of a perspectival system,
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the boundaries of a theory of possible instances,
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or the need for a different structural framing altogether.
In this sense, limits are not external constraints imposed on an otherwise free system. They are internal features of relational structure—exactly the kind of generative limits explored in Impossible Horizons.
Objects as Local Stabilisations
What, then, is an object?
An object is a locally stable node in a network of relations—a position that remains invariant across a family of cuts. Its apparent persistence is not intrinsic; it is relationally maintained.
Seen this way:
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identity is perspectival,
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individuation is structural,
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and stability is always provisional.
From Horizons to Structure
Impossible Horizons showed us that possibility is unbounded, recursive, and generative. Category Cuts does not retreat from that openness. Instead, it asks how such openness can be structurally articulated without being closed.
Categories offer one answer: not as foundations, but as formalisations of constraint—ways of speaking precisely about how perspectives relate, compose, and fail.
In the next post, we will move from categories themselves to the relations between categories, exploring functors as perspectival shifts: how one theory of possible instances can be taken up within another without reduction or collapse.
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