nLab
compact object - contents

objects $d\in C$ such that $C(d,-)$ commutes with certain colimits

• coproduct-preserving representable

• connected object

• compact object

  • compact object in a (0,1)-category, compact object in an (∞,1)-category

  • finite object

  • small object

• tiny object

• atomic object

  • amazing right adjoint

• accessible category

  • presentable category

Models

• compact topos

• compact topological space

Relative version

• proper geometric morphism

• proper map

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