cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A384135 Number of Cauchy-complete categories with n morphisms.

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%I A384135 #9 May 22 2025 10:53:00
%S A384135 1,2,4,11,25,63,163,451,1311
%N A384135 Number of Cauchy-complete categories with n morphisms.
%C A384135 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.
%H A384135 Geoff Cruttwell, <a href="https://www.reluctantm.com/gcruttw/publications/ams2014CruttwellCountingFiniteCats.pdf">Counting Finite Categories</a>, presentation, (2018).
%H A384135 nLab, <a href="https://ncatlab.org/nlab/show/Cauchy+complete+category">Cauchy complete category</a>.
%H A384135 nLab, <a href="https://ncatlab.org/nlab/show/Karoubi+envelope">Karoubi envelope</a>.
%Y A384135 Cf. A125697.
%K A384135 nonn,hard,more
%O A384135 1,2
%A A384135 _Elijah Beregovsky_, May 20 2025