Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functorial approach to Gabriel $k$-quiver constructions for coalgebras
  and pseudocompact algebras   We define the path coalgebra and Gabriel quiver constructions as functors
between the category of $k$-quivers and the category of pointed $k$-coalgebras,
for $k$ a field. We define a congruence relation on the coalgebra side, show
that the functors above respect this relation, and prove that the induced
Gabriel $k$-quiver functor is left adjoint to the corresponding path coalgebra
functor. We dualize, obtaining adjoint pairs of functors (contravariant and
covariant) for pseudocompact algebras. Using these tools we describe precisely
to what extent presentations of coalgebras and algebras in terms of path
objects are unique, giving an application to homogeneous algebras.

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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol