A384135 Number of Cauchy-complete categories with n morphisms.

1, 2, 4, 11, 25, 63, 163, 451, 1311

Offset: 1

Author

Elijah Beregovsky, May 20 2025

Keywords

• nonn
• hard
• more

Comments

A Cauchy-complete (also called Karoubi-complete or idempotent-complete) category is one in which all idempotents split. In other words, in a Cauchy-complete category every arrow e:A→A such that e=e∘e has a retract, meaning there exists an object B and morphisms r:A→B and s:B→A such that s∘r=e but r∘s=1_B.

Links

• Geoff Cruttwell, Counting Finite Categories, presentation, (2018).
• nLab, Cauchy complete category.
• nLab, Karoubi envelope.

Crossrefs

Cf. A125697.