Whilst the relationship between initial algebras and monads is well understood, the relationship between final coalgebras and comonads is less well explored. This paper shows that the problem is more… (More)

This paper introduces guarded and strongly guarded monads as a unified model of a variety of different term algebras covering fundamental examples such as initial algebras, final coalgebras, rational… (More)

Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is… (More)

Non-well-founded trees are used in mathematics and computer science, for modelling non-well-founded sets, as well as non-terminating processes or infinite data structures. Categorically, they arise… (More)

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on finitely… (More)

Motivated by a desire to gain a better understanding of the “dimensionby-dimension” decompositions of certain prominent monads in higher category theory, we investigate descent theory for… (More)

There are several approaches to the problem of giving a categorical semantics to Martin-Löf type theory with dependent sums and products and extensional equality types. The most established one… (More)

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories… (More)