%0 Conference Proceedings
%T Approximate Coalgebra Homomorphisms and Approximate Solutions
%+ Czech Technical University in Prague (CTU)
%A Adámek, Jiří
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 15th International Workshop on Coalgebraic Methods in Computer Science (CMCS)
%C Dublin, Ireland
%Y Daniela Petrişan
%Y Jurriaan Rot
%I Springer International Publishing
%3 Coalgebraic Methods in Computer Science
%V LNCS-12094
%P 11-31
%8 2020-04-25
%D 2020
%R 10.1007/978-3-030-57201-3_2
%Z Computer Science [cs]Conference papers
%X Terminal coalgebras $$\nu F$$ of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their underlying sets. The subspace formed by the initial algebra $$\mu F$$ has the property that for every coalgebra A we obtain its unique homomorphism into $$\nu F$$ as a limit of a Cauchy sequence of morphisms into $$\mu F$$ called approximate homomorphisms. The concept of a strongly lfp category includes categories of sets, posets, vector spaces, boolean algebras, and many others.For the free completely iterative algebra $$\varPsi B$$ on a pointed object B we analogously present a canonical ultrametric on its underlying set. The subspace formed by the free algebra $$\varPhi B$$ on B has the property that for every recursive equation in $$\varPsi B$$ we obtain the unique solution as a limit of a Cauchy sequence of morphisms into $$\varPhi B$$ called approximate solutions. A completely analogous result holds for the free iterative algebra RB on B.
%G English
%Z TC 1
%Z WG 1.3
%2 https://inria.hal.science/hal-03232353/document
%2 https://inria.hal.science/hal-03232353/file/493577_1_En_2_Chapter.pdf
%L hal-03232353
%U https://inria.hal.science/hal-03232353
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-WG1-3
%~ IFIP-CMCS
%~ IFIP-LNCS-12094