A 2-categorial Generalization of the Concept of Institution

After defining, for each many-sorted signature Σ = (S, Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for \mathbb T_S{\mathbb {T}_{\bf \Sigma}}, the monad in Set ^S determined by the adjunction T_S \dashv G_S{{\bf T}_{\bf \Sigma} \dashv {\rm G}_{\bf \Sigma}} from Set ^S to Alg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor d_à{{\bf d}_\diamond} from Ter(Σ) to Ter(Λ). Once defined the mappings that assign, respectively, to a many-sorted signature the corresponding category of generalized terms and to a signature morphism the functor between the associated categories of generalized terms, we state that both mappings are actually the components of a pseudo-functor Ter from Sig to the 2-category Cat. Next we prove that there is a functor Tr^Σ, of realization of generalized terms as term operations, from Alg(Σ) × Ter(Σ) to Set, that simultaneously formalizes the procedure of realization of generalized terms and its naturalness (by taking into account the variation of the algebras through the homomorphisms between them). We remark that from this fact we will get the invariance of the relation of satisfaction under signature change. Moreover, we prove that, for each signature morphism d from Σ to Λ, there exists a natural isomorphism θ ^d from the functor Tr^L °(Id ×d_à){{{\rm Tr}^{\bf {\bf \Lambda}} \circ ({\rm Id} \times {\bf d}_\diamond)}} to the functor Tr^S °(d^* ×Id){{\rm Tr}^{\bf \Sigma} \circ ({\bf d}^* \times {\rm Id})}, both from the category Alg(Λ) × Ter(Σ) to the category Set, where d* is the value at d of the arrow mapping of a contravariant functor Alg from Sig to Cat, that shows the invariant character of the procedure of realization of generalized terms under signature change. Finally, we construct the many-sorted term institution by combining adequately the above components (and, in a derived way, the many-sorted specification institution), but for a strict generalization of the standard notion of institution.     

Knowledge and Justice: A Comment

ABSTRACT

Epistemic justice projects are now one of the most important sites of science studies scholarship and engagement. The papers in this collection make clear that we divorce science and technology from questions of power at our peril, if we are to understand what generates and remediates the inequalities that past and extant knowledge creation and distribution systems have wrought. Expertise and experts are the conceptual anchors for these articles, and they offer quite different perspectives on whether expertise and counter-expertise are the terrain on which epistemic justice struggles ought to be fought. Some challenge older conceptualizations of expertise as narrow and specific, providing new evidence and frameworks for treating epistemes that are heterogeneous and boundary-crossing as means to justice; others demonstrate that acting on concerns as purely technical matters can provide strategic advantages; and others make clear that formally trained experts are neither welcome nor visible in technopolitical justice struggles. Reflected in the innovative approaches that the papers take, a second major contribution of the collection is to show why inclusion is itself a just goal, and a means to uncovering stories of injustice, technical innovations, and visions of the future that can offer new pathways to justice. The collection inspires new directions in sts, including which stories, and by whom, matter and why, and how attention to innovation can be balanced with attention to the extant, and to history.