Category Theory Through the Lens of Relational Ontology: 5 Higher-Order Relationality: When Alignments Themselves Become Horizons

Up to this point we have reinterpreted the basic machinery of category theory through a relational-ontological lens:

• A category is not an object-first universe but a systemic horizon of potential—a patterned space of relations.

• A morphism is an actualisation pathway: a cut through this horizon that enacts one potential configuration.

• A functor is a cross-scale alignment: a construal of one horizon through another.

• A natural transformation is a modulation of alignment: a relational tuning between construals, preserving coherence across traversals.

This brings us now to the next structural threshold:

What happens when these alignments and modulations no longer operate merely on fixed horizons, but become horizons in their own right?

Category theory names this shift the move to higher categories.

Relational ontology frames it as the emergence of relational strata: layers of meaning constituted not by objects or events but by relations between relations, construals of construals.

This post explores how higher-order relationality becomes an inevitable—and structurally necessary—extension of the relational stance.

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1. When Construal Requires Its Own Horizon

A natural transformation is already a second-level entity:

not a relation in $\mathcal{C}$ or $\mathcal{D}$, but a relation between two ways of relating $\mathcal{C}$ to $\mathcal{D}$.

But once we recognise these modulations as structured potentials—coherent, repeatable, composable—something becomes clear:

Modulations of alignment form a relational system of their own.

They have:

• compositional possibilities,

• internal coherences,

• potentials for further modulation.

In other words: they exhibit horizon-like properties.

Category theory formalises this by treating functors as objects and natural transformations as morphisms of a new category:

$$[\mathcal{C},\mathcal{D}]$$

the functor category.

From a relational-ontological perspective, this is nothing more than acknowledging that:

Every coherent relational practice can itself be construed as a horizon of potentials.

Once you adopt relation as primary, this layering is not optional.

It is structurally inevitable.

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2. Functor Categories: Construals as First-Class Citizens

In the functor category $[\mathcal{C}, \mathcal{D}]$, we treat functors as objects and natural transformations as morphisms.

But this is not a shift in ontology; it is a shift in perspectival level.

What previously were:

• alignments between horizons,
  now become:

• the horizon under consideration.

We have moved to a domain where the meaning-making practices themselves—the construals and modulations—are the relata.

This is the formal reflection of what relational ontology asserts about meaning:

Meaning is constituted by patterns of construal, and these patterns form their own ecological systems.

Thus a functor category is an ecological space of construal-relations.

It is the categorical analogue of a meta-semiotic horizon: a horizon of ways of making meaning.

In Hallidayan terms, this would correspond to the metafunctional stratum of meaning about meaning, without collapsing into Martin’s confusion of contextual and semiotic orders.

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3. 2-Categories: Modulating the Modulations

The next step is to recognise that even natural transformations can enter into higher-order relations—so-called modifications in a 2-category.

But again, from the relational stance, this is simply the next logical move:

If alignments can be modulated, then those modulations can themselves be modulated.

Each level is nothing but the previous level seen as a horizon, with potentials to be traversed, aligned, constrained, and modulated.

A 2-category therefore reflects a third-order relational ecology, in which:

• objects are horizons,

• 1-morphisms are cross-horizon alignments,

• 2-morphisms are modulations of those alignments.

This structure mirrors the relational ontology’s commitment to meaning as endlessly perspectival and inherently stratified—not in the sense of being “stacked representations,” but in the sense that relations can be construed, and those construals can themselves be brought into relational practice.

This is not abstraction for its own sake.

It is the natural consequence of treating relation as primary.

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4. The Relational Principle: Horizons All the Way Up

Higher categories often elicit the question:

Why keep adding more layers? Aren’t 2-morphisms already enough?

But the relational ontology supplies a clean answer:

As long as there is room to construe construals, the structure remains open to further individuation.

Each new layer:

• is not imposed,

• is not an artefact of mathematical flourish,

• is not representational overhead.

Instead, each layer emerges whenever:

• a practice of alignment becomes sufficiently stable,

• its internal modulations form coherent pathways,

• and those pathways demand their own systemic articulation.

This is the exact logic of semantic stratification in language:

• semantics is not reducible to context,

• and metafunctions are not reducible to semantics,
  because each level is a horizon with its own systemic potentials.

Category theory simply provides the most elegant expression of the same dynamic.

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5. The Philosophical Consequence: Mind as a Higher-Order Relational Stack

Once we see that horizons generate further horizons through stable relational practice, the ontology of mind becomes sharply clear:

• Mind is not inside the organism.

• Mind is not the sum of cognitive functions.

• Mind is not an inner representational engine.

Rather:

Mind is the multi-tiered ecology of how relational potentials are aligned, modulated, cross-scaled, and recursively integrated.

Higher-order relationality is not a metaphor for mind;

mind is higher-order relationality.

The stratification of construal is the stratification of consciousness.

This insight will be the basis for the concluding posts of the series.

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6. Toward Post 6: Bicategories and the Softness of Systemic Horizons

Having established that construals of construals produce new horizons, the next question is:

What happens when these horizons are not strictly rigid?

Category theory answers with bicategories and more flexible higher structures.

Relational ontology interprets this as:

• the softening of systemic boundaries,

• the emergence of non-strict horizon alignment,

• and the ecology of perspective that does not resolve into a single canonical cut.

This is the subject of Post 6.