Coalgebra-to-Algebra Morphisms

Coalgebra-to-Algebra Morphisms

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

Deformations of Coalgebra Morphisms

An algebraic deformation theory of coalgebra morphisms is constructed.

Coalgebra Morphisms Subsume Open Maps

Algebra of Morphisms

Let I be a set and let A, f be functions. The functor f↾IA yielding a many sorted function indexed by I is defined by: (Def. 1) For every set i such that i ∈ I holds (f↾IA)(i) = f↾A(i). One can prove the following propositions: (1) For every set I and for every many sorted set A indexed by I holds idUnionA↾IA = idA. (2) Let I be a set, A, B be many sorted sets indexed by I, and f , g be functio...

Initial Algebra and Final Coalgebra Semantics

The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial semantics from final semantics, using the initiality and finality to ensure their equality. Moreo...