PlanetPhysics/Compact Object

Let us consider an [[../DenseSubcategory/|additive category]] $𝒜$ with arbitrary direct sums (also called coproducts ).

An [[../TrivialGroupoid/|object]] $X$ of $𝒜$ is called compact if, for an arbitrary set of objects of $𝒜$ and a [[../TrivialGroupoid/|morphism]] $f:X\to \underset{\alpha \in I}{⨁}{M}_{\alpha },$ there exists some finite set $S\subset I$ such that $Imf$ is a subobject of $\alpha \in \underset{\alpha \in S}{⨁}{M}_{\alpha }.$