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

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

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

Examples

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)