Continues from The graphical moves of projective conical spaces (I).

In this post we see the list of moves.

The colours X and O are added to show that the moves preserve the class of graphs PROJGRAPH.

The drawing convention is the following: columns of colours represent possible different choices of colouring. In order to read correctly the choices, one should take, for example, the first elements from all columns, as a choice, then the second element from all columns, etc. When there is only one colour indicated, in some places, then there is only one choice for the respective arrow. Finally, I have not added symmetric choices obtained by replacing everywhere X by O and O by X.

**1. The PG move.**

As you see, there is only one PG move. There are 3 different choices of colours, which results into 3 versions of the PG move, as explained in the post A simple explanation with types of the hexagonal moves of projective spaces.

**2. The DIST move.**

This is the projective version of the “mystery” move which appeared in the posts

- Dictionary from emergent algebra to graphic lambda calculus (I)
- Dictionary from emergent algebra to graphic lambda calculus (II)
- Dictionary from emergent algebra to graphic lambda calculus (III)

Look at the chemlambda DIST moves to see that this move is in the same family.

**3. The R1 move.**

This is a projective version of the GLC move R1 (more precisely R1a). The name comes from “Reidemeister 1” move, as seen through the lens of emergent algebras.

**4. The R2 move.**

This is a projective version of the GLC move R2 . The name comes from “Reidemeister 2” move.

**5. The ext2 move.**

This is a projective version of the **GLC move ext2**.

**6. CO-COMM, CO-ASSOC and LOC PRUNING.** These are the usual moves associated to the fanout node. The LOC PRUNING move for the dilation node is also clear.

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All these moves are local!

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