mathematical structure
additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance
enriched category
category whose hom sets have additional structure
orientation of a vector bundle
generalization of an orientation of a vector space
CW complex
type of topological space
orientation
definition of "clockwise" in a mathematical space
(B, N) pair
structure on Lie groups
concrete category
category equipped with a faithful functor to the category of sets
differentiable manifold
manifold upon which it is possible to perform calculus (any differentiablity class)
capacity
nonadditive generalization of measure
approach space
set equipped with a point-to-subset distance function
partially ordered space
topological space equipped with a closed partial order
algebraic structure
set equipped with one or more finitary operations defined on it
uniform space
set given a measure of "closedness" of two points
divided power structure
concept in commutative algebra
cut locus
mathematical structure
Substructure
structure in mathematical logic
class
mathematical collection of sets that can be defined based on a property of its members (set theory)
principal bundle
fiber bundle whose fibers are group torsors (groups with the identity element forgotten)
exponential object
categorical generalization of a function space in set theory
structure in differential geometry
mathematical structure
diagram
collection of objects and morphisms in a category
differential structure
mathematical structure
monoid object
monoid in certain category-theoretic category
factorization system
category theory generalization of fumction factorization
G-structure
structure group sub-bundle on a tangent frame bundle
internal category
structure, with properties similar to a (small) category, constructed inside any category with pullbacks; two objects O (objects) and M (morphisms), equipped with arrows s, t: M → O (source/target), e: O → M (identity), m: M ₛ×ₜ M → M (composition)
smooth structure
a maximal smooth atlas for a topological manifold
connection
operation on fibered manifolds
level structure
extra structure attached to a space that rigidifies the space, i.e. such that the automorphism group of X preserving this structure is trivial
proximity space
set equipped with structure describing a notion of "nearness" between subsets
triangulated category
category with the additional structure of a translation functor and a class of distinguished triangles
weak n-category
generalization of the strict notion of n-category
computer arithmetic
type of arithmetic that uses computer representation of numbers