# Category:Isomorphisms

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This category contains results about Isomorphisms in the context of Abstract Algebra.

Definitions specific to this category can be found in Definitions/Isomorphisms.

An **isomorphism** is a homomorphism which is a bijection.

That is, it is a mapping which is both a monomorphism and an epimorphism.

## Subcategories

This category has the following 12 subcategories, out of 12 total.

### A

### E

### F

### G

### I

### R

## Pages in category "Isomorphisms"

The following 35 pages are in this category, out of 35 total.

### C

- Composite of Isomorphisms in Algebraic Structure is Isomorphism
- Composite of Isomorphisms is Isomorphism
- Composite of Isomorphisms is Isomorphism/Algebraic Structure
- Composite of Isomorphisms is Isomorphism/R-Algebraic Structure
- Construction of Inverse Completion/Quotient Mapping to Image is Isomorphism

### I

- Inverse of Algebraic Structure Isomorphism is Isomorphism
- Inverse of Algebraic Structure Isomorphism is Isomorphism/General Result
- Isomorphism by Cayley Table
- Isomorphism from R^n via n-Term Sequence
- Isomorphism is Equivalence Relation
- Isomorphism of External Direct Products
- Isomorphism of External Direct Products/General Result
- Isomorphism Preserves Associativity
- Isomorphism Preserves Cancellability
- Isomorphism Preserves Commutativity
- Isomorphism Preserves Groups
- Isomorphism Preserves Identity
- Isomorphism Preserves Inverses
- Isomorphism Preserves Left Cancellability
- Isomorphism Preserves Right Cancellability
- Isomorphism Preserves Semigroups
- Isomorphism Theorems