Searching for authors named "Jesse Hughes" – sorted by Relevance.
12 documents found, showing 1 through 10.
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Modal Operators for Coequations
- …this paper, we develop the theory of coequations from a logical viewpoint. To clarify, let G = #G, #, ## be a comonad on E , where G preserves regular monos and E is "coBirkho #" (see Definition 2.1). A coequation # over a set C of colors is a regular subobject of GC, the carrier of the cofree…
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Admissible Digit Sets and a Modified Stern-Brocot Representation
- …We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a nite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sucient conditions that such a \digit …
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Simulations in Coalgebra
- …A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of this lifted functor, an…
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The Coalgebraic Dual Of Birkhoff's Variety Theorem
- …. We prove an abstract dual of Birkho's variety theorem for categories E of coalgebras, given suitable assumptions on the underlying category E and suitable : E ## E . We also discuss covarieties closed under bisimulations and show that they are denable by a trivial kind of coequation { namely,…
- Cited by 10 (0 self) – Add To MetaCart
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Factorization systems and fibrations: Toward a fibred Birkhoff variety theorem
- …It is well-known that a factorization system on a category (with sufficient pullbacks) gives rise to a fibration. This paper characterizes the fibrations that arise in such a way, by making precise the logical structure that is given by factorization systems. The underlying motivation is to obtain g…
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A Thesis Proposal on Final Coalgebras
- …I present an overview of final coalgebras together with a description of initial algebras, showing the analogies between the two. In particular, I show how initiality of algebras leads to the properties of definition by recursion and proof by induction. I then show how final coalgebras have the anal…
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Distributivity of Categories of Coalgebras H. Peter Gumm
- …We prove that for any F the category of F -coalgebras is distributive if F preserves preimages, i.e. pullbacks along an injective map, and that the converse is also true whenever has finite products. 1 …
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Concise Graphs and Functional Bisimulations
- …We investigate the conditions under which least bisimulations exist with respect to set inclusion. In particular, we describe a natural way to remove redundant pairs from a given bisimulation. We then introduce the conciseness property on process graphs, which characterizes the existence of leas…
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Simulations in Coalgebra Jesse Hughes
- …A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of this lifted functor, an…
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A Study of Categories of Algebras and Coalgebras
- …This thesis is intended to help develop the theory of coalgebras by, first, taking classic theorems in the theory of universal algebras and dualizing them and, second, developing an internal logic for categories of coalgebras. We begin with an introduction to the categorical approach to algebras and…
- Cited by 12 (5 self) – Add To MetaCart
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