# Category:Injections

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This category contains results about Injections.

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

## Subcategories

This category has the following 11 subcategories, out of 11 total.

### C

### E

### I

## Pages in category "Injections"

The following 73 pages are in this category, out of 73 total.

### C

- Canonical Injection is Injection
- Cantor-Bernstein-Schröder Theorem
- Cardinality of Image of Injection
- Cardinality of Set of Induced Equivalence Classes of Injection
- Cardinality of Set of Injections
- Cardinality of Set of Injections/Corollary
- Complement of Direct Image Mapping of Injection equals Direct Image of Complement
- Composite of Injection on Surjection is not necessarily Either
- Composite of Injections is Injection
- Composite of Surjection on Injection is not necessarily Either
- Composite of Three Mappings in Cycle forming Injections and Surjection
- Composition of Repeated Compositions of Injections
- Condition for Composite Mapping to be Identity

### D

### E

### I

- Identity Mapping is Injection
- Image of Intersection under Injection
- Image of Set Difference under Injection
- Images of Elements under Repeated Composition of Injection form Equivalence Classes
- Inclusion Mapping is Injection
- Infinite if Injection from Natural Numbers
- Injection from Finite Set to Itself is Permutation
- Injection from Finite Set to Itself is Surjection
- Injection from Finite Set to Itself is Surjection/Corollary
- Injection from Set to Power Set
- Injection has Surjective Left Inverse Mapping
- Injection if Composite is Injection
- Injection iff Left Cancellable
- Injection iff Left Inverse
- Injection iff Monomorphism in Category of Sets
- Injection Induces Total Ordering
- Injection Induces Well-Ordering
- Injection is Bijection iff Inverse is Injection
- Injection to Image is Bijection
- Internal Group Direct Product is Injective
- Intersection of Injective Image with Relative Complement
- Inverse Element of Injection
- Inverse Image Mapping of Injection is Surjection
- Inverse of Injection is Many-to-One Relation
- Inverse of Injection is One-to-One Relation

### M

### P

- Preimage of Image of Subset under Injection equals Subset
- Preimage of Subset of Cartesian Product under Injection from Factor
- Projection from Product of Family is Injection iff Other Factors are Singletons
- Projection is Injection iff Factor is Singleton
- Projection is Injection iff Factor is Singleton/Family of Sets
- Projection is Injection iff Factor is Singleton/Family of Sets/Necessary Condition
- Projection is Injection iff Factor is Singleton/Family of Sets/Sufficient Condition