42,102 research outputs found
Classifying spaces of algebras over a prop
We prove that a weak equivalence between cofibrant props induces a weak
equivalence between the associated classifying spaces of algebras. This
statement generalizes to the prop setting a homotopy invariance result which is
well known in the case of algebras over operads. The absence of model category
structure on algebras over a prop leads us to introduce new methods to overcome
this difficulty. We also explain how our result can be extended to algebras
over colored props in any symmetric monoidal model category tensored over chain
complexes.Comment: Final version, to appear in Algebraic \& Geometric Topolog
On the geometric theory of local MV-algebras
We investigate the geometric theory of local MV-algebras and its quotients
axiomatizing the local MV-algebras in a given proper variety of MV-algebras. We
show that, whilst the theory of local MV-algebras is not of presheaf type, each
of these quotients is a theory of presheaf type which is Morita-equivalent to
an expansion of the theory of lattice-ordered abelian groups. Di
Nola-Lettieri's equivalence is recovered from the Morita-equivalence for the
quotient axiomatizing the local MV-algebras in Chang's variety, that is, the
perfect MV-algebras. We establish along the way a number of results of
independent interest, including a constructive treatment of the radical for
MV-algebras in a fixed proper variety of MV-algebras and a representation
theorem for the finitely presentable algebras in such a variety as finite
products of local MV-algebras.Comment: 52 page
On geometrically equivalent S-acts
In this paper, considering the geometric equivalence for algebras of a
variety of S-acts over a monoid S, we obtain representation theorems
describing all types of the equivalence classes of geometrically equivalent
S-acts of varieties over groups S.Comment: 13 pages, some statements were corrected and improve
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