Category Theory Through the Lens of Relational Ontology: Concluding Summary Post: The Infinite Softness of Structure

Category theory was introduced as the mathematics of what happens between things, but the series has pushed one step further: from “between” to constitutive of. What matters is not the entities but the patterns of potential that make entities possible at all. The posts traced this shift—from the relational axiomatics of objects and arrows, through the perspectival actualisation encoded by morphisms, all the way to infinite ladders of higher-order relationality where the very horizon of the system becomes soft, revisable, and open.

Across this arc, four themes crystallised:

1. The primacy of relational potential – Nothing begins with objects; everything begins with the way potentials align, cut, and oscillate to yield instances.

2. Actualisation as morphic pathway – Arrows do not connect pre-given items; they are the act of carving instances from system-potential.

3. Cross-scale coherence – Functors and natural transformations articulate how relational horizons can translate, modulate, and re-align without collapsing into object-based metaphysics.

4. Soft hierarchies without closure – Bicategories, ∞-categories, and related structures expose a cosmos that never “bottoms out,” because relational potential is inexhaustible and no perspective can finalise it.

We end not with a system, but with a stance:

A willingness to treat every boundary as provisional, every instance as perspectival, and every coherence as something accomplished—never guaranteed.

This is the open relational cosmos: infinitely deep, endlessly soft, and always already meaning-bearing in its very mode of actualisation.

The next step is to ask how semiosis emerges from this cosmos—not as a layer added on top, but as a mode of relational orientation that discovers itself as both event and theory-in-practice.