Relational ontology meets category theory — gently, playfully, and without mercy.
Page 1 —
Liora woke up to find a tiny envelope beside her pillow.
It shimmered with the colour of “almost”.
Inside was a note:
“Dear Liora,
Some of your cuts have drifted into my neighbourhood.
Please come visit.
— Professor Arrow”
Page 2 —
Liora followed the note’s glow until she stepped into a place unlike any other.
Everywhere she looked, there were things—
but not things, exactly.
They were Somethings inside little bubbles.
“Welcome to Category Land!” said a crisp voice.
Page 3 —
A long, thin creature swooped in—
sharp at both ends, glowing in the middle.
“I’m Arrow,” it said.
“I don’t live anywhere—
I go from one thing to another.
That’s what we do here.”
Page 4 —
Liora pointed to a bubble labelled A.
“Is that a thing?”
Arrow shook its head.
“No, no. It’s an object.
Objects don’t do much alone.
What matters is how they connect.”
Page 5 —
Arrow zoomed between bubble A and bubble B.
A radiant line appeared behind it.
“This,” it said proudly,
“is a morphism.
We’re all about the relations, not the stuff.”
Liora grinned.
“You’d get along with Potentia.”
Page 6 —
Just then, Potentia peeked into view, wobbling happily.
“I told you this place would feel familiar!
Everything here is made of how things relate,
not what they are.”
Page 7 —
A soft humming surrounded them.
Two bubbles glided closer,
and their arrows lined up neatly.
Arrow whispered,
“Watch… composition.”
With a sparkle—
A → B → C
became
A → C.
“Ta-daaaa!
This is how we build pathways through possibility.”
Page 8 —
A wise old diagram glided over.
Its name tag read Functor.
It wore a graduation cap and a knowing smile.
“I carry whole patterns from one category to another,”
Functor said.
“I don’t move objects—
I move the relations between objects.”
Page 9 —
Liora gasped.
“So you mean… the shape of the relating stays the same?”
“Precisely,” said Functor.
“We preserve the structure of cuts.”
Page 10 —
Potentia clapped.
“It’s like when a tree becomes a melody
because the pattern of its branching
matches the pattern of the song’s rhythm!”
Functor beamed.
“Exactly, my shimmering friend.”
Page 11 —
Suddenly the sky rearranged itself into a big commutative diagram.
Shapes floated in place: squares, triangles, pentagons—
each filled with objects and arrows.
Arrow whispered,
“These are our promises.
If you follow one path or another,
you end up in the same place.”
Page 12 —
Liora blinked.
“That sounds… honest.”
“That’s the idea,” Functor said.
“We make sure everything fits,
so the world doesn’t wobble apart.”
Potentia giggled.
“I do love a well-behaved wobble.”
Page 13 —
Then a bright little loop bounded over, squeaking excitedly.
“I’m Identity!” it said.
“I stay right where I am—
but everything needs me!”
Arrow sighed fondly.
“Yes, yes.
Identity keeps every object grounded.
Otherwise arrows would get lost.”
Page 14 —
They approached a shimmering canyon labelled Limit.
“What’s that?” Liora asked.
Functor whispered,
“It’s where many relations come together
to form one perfect summarising relation.”
“Like gathering clues,” said Potentia,
“to slice the world just right.”
Page 15 —
Across the canyon was another glow: Colimit.
“That’s where many pieces spread out
into the fullest thing they can become,”
Arrow explained.
“Like letting a dream unfold,” Potentia sighed.
Page 16 —
As they wandered, the landscape blurred—
objects melting into relations,
relations melting into patterns,
patterns melting into higher-patterns.
Liora could feel it:
Category Land wasn’t things.
It was a grammar for potential.
Page 17 —
Liora asked quietly,
“Is this place… real?”
Arrow smiled.
“As real as any cut you make.
Category Land is what happens
when you look not at what something is,
but at how it connects.”
Page 18 —
Potentia shimmered beside her.
“And that’s why you’re here, Liora.
You see the world as relation-first.
Category Land simply speaks your language.”
Page 19 —
As they turned to leave, Functor handed Liora a tiny chalkboard.
“For drawing patterns,” they said.
“Remember—
a world becomes clear
when its relations do.”
Final Page —
Back home, Liora smiled.
The Land of Maybe and Category Land
were two sides of the same shimmering truth:
what something is
depends on how it connects.
And that night, she fell asleep
dreaming of arrows,
cutting through possibility,
tracing new ways
for the world to happen.
