Characterization of protomodular varieties of universal algebras.
Clone properties of topological spaces
Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.
Clones in topology and algebra.
Closedness properties of internal relations. IV: Expressing additivity of a category via subtractivity.
Colimits of representable algebra-valued functors.
Complétion et complétude selon H. Andreka et I. Nemeti
Congruence relations on finitary models
Construction of all strong homomorphisms of binary structures
Dualities for Stone algebras, double Stone algebras, and relative Stone algebras
Duality for some free modes
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.
Equimorphy in varieties of double Heyting algebras
We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive...
Exponentiality in categories of partial algebras.
Finitely generated universal varieties of distributive double -algebras
Finite-to-finite universal varieties of distributive double -algebras
Free algebras in varieties
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.
From hereditary classes to varieties in abstract model theory and partial algebra
Generalization of the concept of variety and quasivariety to partial algebras through category theory [Book]
Good functors... are those preserving philosophy !
Hereditary properties of algebras with respect to inductive limits
Homomorphisms of heterogeneous algebras
A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].