Contents

category theory

(0,1)-category

(0,1)-topos

# Contents

## Idea

The notion of a partially ordered object is the generalization of that of partially ordered sets as one passes from the ambient category of sets into more general ambient categories with suitable properties.

## Definitions

In a finitely complete category $C$, a partially ordered object is a preordered object $(X, R, s, t, \rho, \tau_p)$ such that the internal preorder $R\stackrel{(s,t)}\hookrightarrow X \times X$ is an internal antisymmetric relation.