Sketch (mathematics) explained
In the mathematical theory of categories, a sketch is a category D, together with a set of cones intended to be limits and a set of cocones intended to be colimits. 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.
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