Algebraic cocompleteness and finitary functors

A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and, more generally, all precontinuous) set functors the initial algebra and terminal coalgebra are proved to carry a canonical partial order with the same ideal CPO-completion. And they also both carry a canonical ultrametric with the same Cauchy completion

Contrast law building in accordance with new civil code, along imperial code no. 114 from of the day 11. June 1912 and status quo – I

Contrast law about a building right according to new civil code and law No. 344/1992 Sb., about real estate register Czech republic (cadastral law), in valid wording, with building right according to No. 114 empire code from of the day 11. June 1912.Porovnání ustanovení o právu stavby dle nového občanského zákoníku a zákona č. 344/1992 Sb., o katastru nemovitostí České republiky (katastrální zákon), v platném znění, s právem stavby dle č. 114 říš. zákoníka ze dne 11. června 1912

Corecursive Algebras, Corecursive Monads and Bloom Monads

An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization of Elgot's iterative monads, analogous to corecursive algebras generalizing completely iterative algebras. We also characterize the Eilenberg-Moore algebras for the free corecursive monad and call them Bloom algebras