Definition 11.3.2.3.1 (00YH): Connected Categories — The Clowder Project

Table of Contents
Part 4: Categories
Chapter 11: Categories
Section 11.3: The Quadruple Adjunction With Sets
Subsection 11.3.2: Connected Components and Connected Categories
Subsubsection 11.3.2.3: Connected Categories
Definition 11.3.2.3.1: Connected Categories (cite)

11.3.2.3 Connected Categories

Definition 11.3.2.3.1 ▶ Connected Categories

A category $\mathcal{C}$ is connected if $\pi _{0}(\mathcal{C})\cong \mathrm{pt}$.^1,2

¹Further Terminology: A category is disconnected if it is not connected.
²Example: A groupoid is connected iff any two of its objects are isomorphic.

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