In
category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
, a branch of mathematics, an opetope, a portmanteau of "
operation
Operation or Operations may refer to:
Arts, entertainment and media
* ''Operation'' (game), a battery-operated board game that challenges dexterity
* Operation (music), a term used in musical set theory
* ''Operations'' (magazine), Multi-Man ...
" and "
polytope
In elementary geometry, a polytope is a geometric object with flat sides ('' faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an ...
", is a
shape
A shape is a graphics, graphical representation of an object's form or its external boundary, outline, or external Surface (mathematics), surface. It is distinct from other object properties, such as color, Surface texture, texture, or material ...
that captures higher-dimensional
substitution
Substitution may refer to:
Arts and media
*Substitution (poetry), a variation in poetic scansion
* Substitution (theatre), an acting methodology
Music
*Chord substitution, swapping one chord for a related one within a chord progression
*Tritone ...
s. It was introduced by
John C. Baez and James Dolan so that they could define a
weak ''n''-category as a certain
presheaf
In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the d ...
on the category of opetopes.
See also
*
higher-order operad
References
*
External links
*
Category theory
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