# Contents

## Definition

If $C$ is a category than an ind-object $x\in Ind(C)$ is a strict ind-object if it can be represented in $Ind(C)$ as the (vertex of) a colimit of a small filtered diagram whose objects are in $C$ and morphisms are monomorphisms in $C$.

An ind-object isomorphic in $Ind(C)$ to a strict ind-object is sometimes called essentially monomorphic. A pro-object isomorphic in $Pro(C)$ to a strict pro-object is sometimes called essentially epimorphic. (This is not so good terminology unless we call strict pro-objects epimorphic which does not seem to be used.)