La apropiación del espacio: una propuesta teórica para comprender la vinculación entre las personas y los lugares

The links between people and places have been explained from several points of view in social science literature. Place-attachment, place-identity, social urban identity, and symbolic urban space are some of the main concepts used to describe the interaction between people and their environments. A dialectical approach to the appropriation of space may be able to address some of these concepts in a more comprehensive way. Besides its impact within the scientific community, the approach is useful in applied questions such as the social construction of public space, civic responsibility, citizenship, and economic, social, and environmental sustainability, and contributes theoretical and empirical elements for fairer and more effective methods of social interaction in accordance with new social demands

When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

For a set of sorts S and an S-sorted signature Σ we prove that a profinite Σ-algebra, i.e. a projective limit of a projective system of finite Σ-algebras, is a retract of an ultraproduct of finite Σ-algebras if the family consisting of the finite Σ-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the final sections of it, we show that there exists a functor from the just mentioned category whose object mapping assigns to an object a natural transformation which is a retraction

Eilenberg Theorems for Many-sorted Formations

A theorem of Eilenberg establishes that there exists a bijectionbetween the set of all varieties of regular languages and the set of all vari-eties of finite monoids. In this article after defining, for a fixed set of sortsSand a fixedS-sorted signature Σ, the concepts of formation of congruenceswith respect to Σ and of formation of Σ-algebras, we prove that the alge-braic lattices of all Σ-congruence formations and of all Σ-algebra formationsare isomorphic, which is an Eilenberg's type theorem. Moreover, under asuitable condition on the free Σ-algebras and after defining the concepts offormation of congruences of finite index with respect to Σ, of formation offinite Σ-algebras, and of formation of regular languages with respect to Σ, weprove that the algebraic lattices of all Σ-finite index congruence formations,of all Σ-finite algebra formations, and of all Σ-regular language formationsare isomorphic, which is also an Eilenberg's type theorem

Functoriality of the Schmidt construction

After proving, in a purely categorial way, that the inclusion functor InAlg(Σ) from Alg(Σ)⁠, the category of many-sorted Σ-algebras, to PAlg(Σ)⁠, the category of many-sorted partial Σ-algebras, has a left adjoint FΣ⁠, the (absolutely) free completion functor, we recall, in connection with the functor FΣ⁠, the generalized recursion theorem of Schmidt, which we will also call the Schmidt construction. Next, we define a category Cmpl(Σ)⁠, of Σ-completions, and prove that FΣ⁠, labelled with its domain category and the unit of the adjunction of which it is a part, is a weakly initial object in it. Following this, we associate to an ordered pair (α,f)⁠, where α=(K,γ,α) is a morphism of Σ-completions from F=(C,F,η) to G=(D,G,ρ) and f a homomorphism of D from the partial Σ-algebra A to the partial Σ-algebra B⁠, a homomorphism Υ G,0α(f):Schα(f)⟶B⁠. We then prove that there exists an endofunctor, Υ G,0α, of Mortw(D)⁠, the twisted morphism category of D⁠, thus showing the naturalness of the previous construction. Afterwards, we prove that, for every Σ-completion G=(D,G,ρ)⁠, there exists a functor ΥG from the comma category (Cmpl(Σ)↓G) to End(Mortw(D))⁠, the category of endofunctors of Mortw(D)⁠, such that ΥG,0⁠, the object mapping of ΥG⁠, sends a morphism of Σ-completion of Cmpl(Σ) with codomain G⁠, to the endofunctor ΥG,0

A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem

A theorem of single-sorted algebra states that, for a closure space (A, J ) and a natural number n, the closure operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure operator on a set A with n ≥ 2, then, for every i, j ∈ IrB(A, J ), where IrB(A, J ) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J , if i < j and {i + 1, . . . , j − 1} ∩ IrB(A, J ) = Ø, then j − i ≤ n − 1. In this article we state and prove the many-sorted counterparts of the above theorems. But, we remark, regarding the first one under an additional condition: the uniformity of the many-sorted closure operator