A beautiful move in projective spaces

The post Axioms for projective conical spaces (towards qubits II)  introduces a generalization of projective spaces to projective conical space. These are a kind of non-commutative version of projective spaces, exactly in the same sense as the one that affine conical spaces are a non-commutative generalization of affine spaces.

That post has been done before the discovery of graphic lambda calculus. [UPDATE: no, I see that it was done after, but GLC was not used in that post.]

Now, the beautiful thing is that all the 4 axioms of projective conical spaces have the same form, if represented according to the same ideas as the ones of graphic lambda calculus.

There will be more about this, but I show you for the moment only how the first part of  (PG1)  looks like, in the original version and in the new version.

new_proj_2

Here is the first part of (PG2) in old and new versions.

new_proj_5

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