This puzzle defines many many operations on strings, which can be deduced from the fact that various diagrams commute. They are as follows:
| Symbol | Description |
|---|---|
| ι | Identity/canonical inclusion |
| fn | Put the nth letter of the alphabet (mod 26) at the beginning of the string. |
| cn | Caesar shift by n letters |
| un | Put the US postal code of the nth state to achieve statehood at the beginning of the string. |
| o | Replace the string with only the letters in odd position. |
| ω | For two inputs, return the string of letters where those two inputs agree. |
| πn | Projection onto nth coordinate |
| δ | Diagonal inclusion |
| r | Reverse a string |
| κ | Concatenate two strings |
| ρ | Riffle shuffle the two strings |
| in,m | Insert the mth letter into the nth position |
| tn | Transpose the first letter and the nth letter |
| dn | Double the nth letter |
| sn | The solfege for the nth note (starting with C) is added to the front |
| en | The atomic symbol for the nth element is added to the front |
| pn | The name of the country with phone dialing code n is added to the front |