coproductpreserving
In category theory, a branch of mathematics, a **coproduct-preserving** functor is a type of functor between categories that respects coproducts. Coproducts, also known as disjoint unions, are a fundamental construction in category theory that generalize the notion of direct sums or disjoint unions of objects. For a functor \( F \): \( \mathcal{C} \rightarrow \mathcal{D} \) between categories \( \mathcal{C} \) and \( \mathcal{D} \), coproduct-preserving means that \( F \) maps coproducts in \( \mathcal{C} \) to coproducts in \( \mathcal{D} \).
Formally, if \( \{A_i\}_{i \in I} \) is a family of objects in \( \mathcal{C} \) with coproduct \( A = \coprod_{i
Coproduct-preserving functors are particularly important in contexts where coproducts play a significant role, such as in
A functor that preserves both products and coproducts is called a **product-coproduct-preserving functor**. Such functors are