In the
mathematical
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
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
In mathematics, specifically category theory, a functor is a Map (mathematics), mapping between Category (mathematics), categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) ar ...
:
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
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...
and its
models
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , .
Models can be divided int ...
. 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.
References
*.
*.
*.
*.
*.
*.
External links
Sketches: Outline with references(updated 2009).
*
Category theory
{{categorytheory-stub