Dissertation/Thesis Abstract

Higher-order algebras and coalgebras
by Kim, Jiho, Ph.D., Indiana University, 2011, 101; 3611486
Abstract (Summary)

In category theory, algebras and coalgebras are abstractions which are often used to reason mathematically about computation. Higher-order instances are now being investigated to deepen our understanding of a diverse set of computational themes such as dependent types, recursive programming schemes, higher-order syntax, etc. The first half of the work investigates a very particular instance of higher-order coalgebras constructed from stream coalgebras. Using this work as motivation, the dissertation proceeds to the complete characterization of initial and final objects in (higher-order) algebra and coalgebra categories which are constructed from parameterized endofunctors on lower-level categories. The result generalizes two results in the literature concerning (1) algebras in arrow categories and (2) coalgebras for iteratable endofunctors. The approach gives a unified view of what is happening in these results and gives a general framework for approaching similar but more specialized higher-order situations.

Indexing (document details)
Advisor: Moss, Lawrence
Commitee: Connell, Christopher, Haghverdi, Esfandiar, Leivant, Daniel
School: Indiana University
Department: Mathematics
School Location: United States -- Indiana
Source: DAI-B 75/05(E), Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Coalgebras, Higher-order algebras, Parameterized endofunctors, Stream coalgebras
Publication Number: 3611486
ISBN: 978-1-303-72311-7
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