The Malcev theorem

Eckstein, Frank

doi:10.1016/0021-8693(69)90038-6

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Covariant Adjoint Functors1

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2020

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Cited by 4 publications

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“…there is a continuous automorphism ψ ∼ id of k [[V Q]] such that γ ψ = δ . The proof of (Iusenko and MacQuarrie 2020, Proposition 6.1) carries through for pseudocompact algebras, using a version for pseudocompact algebras of the Malcev Uniqueness Theorem due to (Eckstein (1969), Theorem 17).…”

Section: Covariant Adjoint Functorsmentioning

confidence: 99%

A Functorial Approach to Gabriel k-quiver Constructions for Coalgebras and Pseudocompact Algebras

Iusenko

MacQuarrie

Quirino

2020

Bull Braz Math Soc, New Series

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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 pseudocompact algebras in terms of path objects are unique, giving an application to homogeneous algebras.

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Section: Covariant Adjoint Functorsmentioning

confidence: 99%