## Smart answer:

# Your search for *′What is the counterpart to injective maps′* returned the following results:

### surjective maps

The counterpart to injective maps are surjective maps (every element of the target is mapped onto), such as the canonical map .

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### a map that designates a unique image for every element

An injective map also called “one-to-one” is a map that designates a unique image for every element.

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### the monomorphisms

The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.

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### g : :} A → P ( A ) {\displaystyle gA\to {\mathcal {P}}(A)} defined by x ↦ { x } {\displaystyle x\mapsto \{x\

On the other hand, g : A → P ( A ) {\displaystyle g:A\to {\mathcal {P}}(A)} defined by x ↦ { x } {\displaystyle x\mapsto \{x\}} is an injective map.

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### the kernel

the kernel is not just an injective map anymore.

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### val

; val injects = maps (#inject o Datatype.the_info thy1) dt_names; Const ('Nominal.fresh_star',

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### an element c

An M-regular element is an element c such that multiplication on the left by c is an injective map

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### to mono- and epimorphisms, respectively

Injective and surjective maps correspond to mono- and epimorphisms, respectively.

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### a complete set of invariants

Symbolically, a complete set of invariants is a collection of maps such that is injective.

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