category theory

# Contents

## Idea

The solution set condition appears as part of the hypothesis in Freyd’s General Adjoint Functor Theorem.

## Statement

A functor $F : C \to D$ satisfies the solution set condition if for every object $Y$ of $D$ there exists a small set $I$ and an $I$-indexed family of morphisms $\{f_i : Y \to F(X_i)\}_{i \in I}$ such that any morphism $h : Y \to F(X)$ can be factored as

$F(t) \circ f_i : Y \stackrel{f_i}{\to} F(X_i) \stackrel{F(t)}{\to} F(X)$

for some $t : X_i \to X$ and some $i$.

This is a smallness condition in that the family is required to be indexed by a small set.

Revised on October 31, 2010 07:35:46 by Kevin V? (149.142.31.131)