A384135 Number of Cauchy-complete categories with n morphisms.

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

Offset

1,2

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

Table of n, a(n) for n=1..9.

Geoff Cruttwell, Counting Finite Categories, presentation, (2018).

nLab, Cauchy complete category.

nLab, Karoubi envelope.

Crossrefs

Cf. A125697.

Sequence in context: A100550 A329707 A071973 * A086424 A122121 A368412

Adjacent sequences: A384132 A384133 A384134 * A384136 A384137 A384138

Keyword

nonn,hard,more

Author

Elijah Beregovsky, May 20 2025

Status

approved