Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic cocompleteness and finitary functors   A number of categories is presented that are algebraically complete and
cocomplete, i.e., every endofunctor has an initial algebra and a terminal
coalgebra. For all finitary (and, more generally, all precontinuous) set
functors the initial algebra and terminal coalgebra are proved to carry a
canonical partial order with the same ideal CPO-completion. And they also both
carry a canonical ultrametric with the same Cauchy completion.

11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin