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Basic concepts of enriched category theory
TLDR
Lack, Ross Street and Wood as discussed by the authors present a mathematical subject classification of 18-02, 18-D10, 18D20, and 18D21 for mathematics subject classification.Abstract:
Received by the editors 2004-10-30. Transmitted by Steve Lack, Ross Street and RJ Wood. Reprint published on 2005-04-23. Several typographical errors corrected 2012-05-13. 2000 Mathematics Subject Classification: 18-02, 18D10, 18D20.read more
Citations
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Journal ArticleDOI
Notions of computation and monads
TL;DR: Calculi are introduced, based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
Book
Category Theory For Computing Science
Michael Barr,Charles Wells +1 more
TL;DR: Sketches for Endofunctors: Catesian Closed Categories, Diagrams, and Toposes.
Proceedings ArticleDOI
Computational lambda-calculus and monads
TL;DR: The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model.
Book
Rings, Modules, and Algebras in Stable Homotopy Theory
Anthony Elmendorf,Michael Cole +1 more
TL;DR: In this paper, the authors introduce the category of Structured ring and module spectra under $S$ and show how to construct a monadic bar construction on a function spectra.
Journal ArticleDOI
On Full Abstraction for PCF
J. M. E. Hyland,C. H. L. Ong +1 more
TL;DR: An order-extensional, order (or inequationally) fully abstract model for Scott's language pcf, based on a kind of game in which each play consists of a dialogue of questions and answers between two players who observe the following principles of civil conversation.
References
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Book
Categories for the Working Mathematician
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
Book
The geometry of iterated loop spaces
TL;DR: In this article, the recognition principle and A? spaces and E? spaces have been discussed and a categorical construction of monoidal categories has been proposed for simplicial spaces and infinite loop sequences.