Examples of coproduct

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We use coproducts in a list-like fashion: the third instance only searches through the right-hand side of coproduct.
Of particular interest is the behaviour of the coproduct, both by itself and with respect to partial products.
For the tensor, three of the four cases are forced by the requirement that tensor should distribute over coproduct.
The implication (ii) to (i) follows because any colimit decomposes into a coproduct of connected colimits.
An alternative approach extends the ideas contained in this paper by considering coproduct-introduction and coproduct-elimination as adjoint.
In passing, a new uniqueness result is given for the lax coproduct.
It is interesting to observe how in this case the standard coproduct construction actually implements a sophisticated mechanism of distributed choice.
Also, we will consider models that include coproduct types, so will work with bicartesian dcc's (cartesian dcc's that have coproducts).
Some basic constructions on sets will be used, like product, coproduct and exponent.
This definition applies to all categories with finite coproducts such that coproduct injections are monomorphic.
The formulation below refrains from the assumption that coproduct injections are monomorphic.
In particular, extensive categories have the property that coproduct injections are monomorphisms, and a coproduct of two monomorphisms is monomorphic.
Combining data types using the coproduct of their signatures comes at a price.
The functions we present here, however, do not inspect where something occurs in a coproduct.
The concurrent connection of two objects without synchronization is their coproduct in the category having appropriate specifications as objects and certain refinements as morphisms.
Note that these formulas have exactly the polarities of the problematic case discussed in the previous section (remembering that is product and is coproduct).
The key idea is to combine expressions by taking the coproduct of their signatures.
The kind of behaviour illustrated above is characteristic of the coproduct in many categories of models that admit cyclic behaviours, like, for instance, transition systems.
First, for reasons of duality, the product of state spaces is a coproduct of transformers, and the hom-object is a coexponent.
Similarly, decisions and coproduct injections are restriction isomorphisms, and thus extensive.

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