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

M:D\rightarrow C

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.

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