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## 1.4 Labels

You can put labels on arrows. Labels are conceptualized as sub- and superscripts on arrows such that they are placed in the usual positions (as `limits'), i.e., `^` reads `above' and `_` `below' on an arrow pointing right. Notice that the positions depend only on the direction of the arrow, the absolute notions of `up', `down', etc. are not important. For example,

>     $\xymatrix@1{ X\ar[r]^a_b & Y & Z\ar[l]^A_B }$

will set ; the `@1` is a special code that can be used for `one-line' diagrams to improve the placement on the line (more such spacing codes are described in section 3.3).

It is possible to use labels that are not single letters, digits, or control sequences: if a simple math formula in the default style (script style) is desired then simply enclose in `{`...`}`. In practice anything can be used as a label as described in section 2.2.

Each label is placed perpendicular to arrow at the point halfway between the centers of the base and target objects. This is usually the most ęsthethic, however, in diagrams where the sizes of the entries vary much it is sometimes nicer to place the label at the center of the actual arrow. This behaviour is requested by inserting a `-` right after the `^` or `_`: was typeset by

>     $\xymatrix@1{
>      A\times B\times C\times D \ar[r]^-{+} &B
>     }$

It becomes without `-`. In fact `-` is in just one of the may possible placings of labels described in section 2.1.

#### Exercise 3.

Typeset the second axiom of category theory as

Answer.

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