# nLab walking structure

## Definition

If X is a type of structure that can be defined in a category, higher category, or category with some sort of structure, then the walking X is an informal term for the free category (resp. higher category, category with suitable structure) containing an X.

More precisely, if $StructCat$ denotes some (higher) category of categories with an appropriate type of structure, then the walking X is an object $[X] \in StructCat$ together with a natural equivalence

$StructCat([X],C) \simeq \{Xs \; in \; C\}$

between the hom-set/category/space from $[X]$ to $C$, for any $C\in StructCat$, and the set/category/space of all Xs in $C$.

## References

• A Café post about walking objects (among other things), including a comment that explains the terminology.

Revised on March 28, 2013 20:42:32 by Ingo Blechschmidt (137.250.162.16)