# Creation Functions

There are two versions of the coproduct constructor. Ordinarily, coproducts will be constructed from a list of structures. These structures are called the *constituents* of the coproduct. A single sequence argument is allowed as well to be able to create coproducts of parameterized families of structures conveniently.

## Creation of Coproducts

### `cop< S₁, S₂, ..., Sₖ >: Str, Str, ... -> Cop, [ Map ]`

### `cop< [ S₁, S₂, ..., Sₖ ] >: [ Str, Str, ... ] -> Cop, [ Map ]`

Given a list or a sequence of two or more structures $S_1$, $S_2$, $\ldots$, $S_k$, this function creates and returns their coproduct $C$ as well as a sequence of maps [$m_1$, $m_2$, $\ldots$, $m_k$] that provide the injections $m_i\colon S_i\rightarrow C$.

## Creation of Coproduct Elements

Coproduct elements are usually created by the injections returned as the second return value from the `cop<>` constructor. The bang (!) operator may also be used but only if the type of the relevant constituent is unique for the particular coproduct.

### `m(e): Map, Elt -> CopElt`

Given a coproduct injection map $m$ and an element of one of the constituents of the coproduct $C$, create the coproduct element version of $e$.

### `C ! e: Cop, Elt -> CopElt`

Given a coproduct $C$ and an element $e$ of one of the constituents of $C$ such that the type of that constituent is unique within that coproduct, create the coproduct element version of $e$.