isomorphism
Form-preserving mapping
Isomorphism is a structural correspondence between two things that preserves essential relationships.
In mathematics, an isomorphism is a mapping between structures that shows them to be fundamentally identical in form, even if their elements differ: The two groups are related by an isomorphism.
The concept extends to any field where underlying patterns matter more than surface appearances—linguistics, biology, sociology.
Two things are isomorphic when they share the same abstract structure: There's an isomorphism between the organization of ant colonies and corporate hierarchies.
Diagram of correspondences
- structure-preservingMaintains relational organization
- topologyStudy of spatial arrangement
- algebraMath using symbols
- kernelSeed or essential core
State of being equal
- one-to-oneExactly paired correspondence
- matchingIdentical in appearance
- parallelEquidistant at all points
- congruenceState of agreement
analogy · mapping · correspondence · identity · sameness · interchangeability · mirror · alignment
State of being beside
- subgraphContained portion of graph
- labeledMarked for identification
- unlabeledWithout identifying markers
- invariantRemaining always constant
complement · planar · bipartite · chromatic · algorithm · matching
Structural similarity through descent
- phylogeneticOf evolutionary relationships
- developmentalRelated to growth stages
Quality of staying unchanged
- transformationThorough change in form
- rotationalConcerning circular movement
- reflectiveCasting back light
- translationalRelating to straight movement
permutation · conservation · geometric · crystallographic · bilateral · radial · structural · self-similarity
mapping
Diagram of correspondences
- structure-preservingMaintains relational organization
- topologyStudy of spatial arrangement
- algebraMath using symbols
equivalence
State of being equal
- one-to-oneExactly paired correspondence
- matchingIdentical in appearance
- parallelEquidistant at all points
congruence · analogy · mapping · correspondence · identity · sameness · interchangeability · mirror · alignment · parity
adjacency
State of being beside
- subgraphContained portion of graph
- labeledMarked for identification
- unlabeledWithout identifying markers
invariant · complement · planar · bipartite · chromatic · algorithm · matching
homology
Structural similarity through descent
- phylogeneticOf evolutionary relationships
- developmentalRelated to growth stages
invariance
Quality of staying unchanged
- transformationThorough change in form
- rotationalConcerning circular movement
- reflectiveCasting back light
translational · permutation · conservation · geometric · crystallographic · bilateral · radial · structural · self-similarity
isomorphismasymmetry
Absence of balanced form
polymorphism · incongruence · mismatch · disparity · discordance
isomorphismheterogeneity
State of being dissimilar
dissimilarity · difference · disparity · incongruity · distinctness