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===Commentary Note 11.10===

===Commentary Note 11.10===

In the case of a 2-adic relation ''F'' ⊆ ''X'' × ''Y'' that has the qualifications of a function ''f'' : ''X'' → ''Y'', there are a number of further differentia that arise:

In the case of a 2-adic relation <math>F \subseteq X \times Y</math> that has the qualifications of a function <math>f : X \to Y,</math> there are a number of further differentia that arise:

:{| cellpadding="4"

{| align="center" cellspacing="6" width="90%"

| ''f'' is "surjective"

|

| iff

| ''f'' is total at ''Y''.

f ~\text{is surjective}

& \iff &

| ''f'' is "injective"

f ~\text{is total at}~ Y.

| iff

| ''f'' is tubular at ''Y''.

f ~\text{is injective}

& \iff &

| ''f'' is "bijective"

f ~\text{is tubular at}~ Y.

| iff

| ''f'' is 1-regular at ''Y''.

f ~\text{is bijective}

& \iff &

f ~\text{is}~ 1\text{-regular at}~ y.

|}

|}