Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algebraic approach to the completions of elementary doctrines   We provide a thorough algebraic analysis of three known completions having a
central role in the exact completions of Lawvere's doctrines: the one adding
comprehensive diagonals (i.e. forcing equality on terms to coincide with the
equality predicate), the one adding full comprehensions and the one adding
quotients. We show that all these 2-adjunctions are 2-monadic and that the
2-monads arising from these adjunctions are all property-like. This entails
that comprehensive diagonals, full comprehensions and quotients are algebraic
properties of an elementary doctrine. Finally, we discuss and present the
distributive laws between these 2-monads.

12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics