nLab
sketch

Contents

Definition

A sketch is a small category with specified limits and colimits.

A model of a sketch is a Set-valued functor preserving the specified limits and colimits.

A category is called sketchable if it is the category of models of a sketch.

The categories of models of sketches are precisely the accessible categories.

A limit-sketch is a sketch with just limits and no colimits specified.

The categories of models of limit-sketches are the locally presentable categories.

References

An overview of the theory is given in

  • Adámek and Rosicky, Locally Presentable and Accessible Categories. Cambridge University Press, Cambridge, 1994.

That not only every sketchable category is accessible but that conversely every accessible category is sketchable is due to

  • Lair, 1981