Sketch (mathematics)

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In the mathematical theory of categories, a sketch is a category D, together with a set of limit cones and a set of colimit cones. A model of the sketch in a category C is a functor

that takes each specified cone to a limit cone in C and each specified cocone to a colimit cocone in C. Morphisms of models are natural transformations. Sketches are a general way of specifying structures on the objects of a category, forming a category-theoretic analog to the logical concept of a theory and its models. They allow multisorted models and models in any category.

Sketches were invented in 1968 by Charles Ehresmann, using a different but equivalent definition. There are still other definitions in the research literature.


  • Adámek, Jiří; Rosický, Jiří (1994), Locally Presentable and Accessible Categories, London Mathematical Society Lecture Note Series, 189, Cambridge: Cambridge University Press, doi:10.1017/CBO9780511600579, MR 1294136  Text " hellliiiiioooooo
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