Quantum Programs as Kleisli Maps Abraham Westerbaan Radboud University Nijmegen Furber and Jacobs have shown in their study of quantum computation that the category of commutative C∗ -algebras and

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A fully abstract semantics for a higher-order functional language with nondeterministic computation A LAN J EFFREY A BSTRACT. This paper is about the relationship between the theory of monadic types and the practice of c

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• Category theory
• Models of computation
• Adjoint functors
• Functional programming
• Logic in computer science
• Denotational semantics
• Lambda calculus
• Cartesian closed category
• Sheaf
• F-algebra
• Kleisli category
• Monad

PDF Document

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• Computer programming
• Adjoint functors
• Software engineering
• Mathematical analysis
• Markov processes
• Probability theory
• Monad
• Probability distribution
• Kleisli category
• Markov chain
• Probability
• Monoidal monad

Preorders on Monads and Coalgebraic Simulations Shin-ya Katsumata and Tetsuya Sato Research Institute for Mathematical Sciences, Kyoto University, Kyoto, , Japan {sinya,satoutet}@kurims.kyoto-u.ac.jp Abstract. W

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• Mathematics
• Topology
• Functional programming
• Monad
• Preorder
• Grothendieck topology
• Kleisli category
• Alexandrov topology
• Adjoint functors
• Category theory
• Order theory

BRICS Basic Research in Computer Science BRICS RSPower et al.: A Representation Result for Free Cocompletions A Representation Result for

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• Functors
• Monad
• Kleisli category
• Limit
• Universal property
• Natural transformation
• Equivalence of categories
• Enriched category
• Cartesian closed category
• Category theory
• Adjoint functors
• Monoidal categories

Compiling Monads ∗ Olivier Danvy, J¨ urgen Koslowski, and Karoline Malmkjær

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• Adjoint functors
• Functional programming
• Models of computation
• Functional languages
• Monad
• Kleisli category
• Denotational semantics
• List comprehension
• Strong monad
• Software engineering
• Computing
• Computer programming

Theory and Applications of Categories, Vol. 21, No. 7, 2008, pp. 118–151. EXTENSIONS IN THE THEORY OF LAX ALGEBRAS Dedicated to Walter Tholen on the occasion of his 60th birthday CHRISTOPH SCHUBERT AND GAVIN J. SEAL A

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• Algebra
• Monad
• Kleisli category
• Functor
• Group action
• Grothendieck topology
• Allegory
• Universal property
• Adjoint functors
• Abstract algebra
• Category theory

Theory and Applications of Categories, Vol. 28, No. 15, 2013, pp. 403–433. TENSORS, MONADS AND ACTIONS Dedicated to the memory of Pawel Waszkiewicz GAVIN J. SEAL Abstract. We exhibit sufficient conditions for a monoid

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• Abstract algebra
• Monoidal monad
• Monoidal functor
• Monad
• Monoidal natural transformation
• Braided monoidal category
• Kleisli category
• Monoid
• Adjoint functors
• Category theory
• Monoidal categories
• Algebra

Theory and Applications of Categories, Vol. 27, No. 11, 2012, pp. 222–241. THE ∗-AUTONOMOUS CATEGORY OF UNIFORM SUP SEMI-LATTICES Dedicated to the memory of Heinrich Kleisli, 1930–2011. MICHAEL BARR, JOHN F. KENNI

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• Topological spaces
• Functors
• Category
• Coproduct
• *-autonomous category
• Grothendieck topology
• Initial and terminal objects
• Natural transformation
• Additive category
• Category theory
• Abstract algebra
• Mathematics

i i 10 MONADS AND ALGEBRAS

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• Monad
• Functor
• Limit
• Natural transformation
• Sheaf
• Grothendieck topology
• Kleisli category
• Universal property
• Adjoint functors
• Category theory
• Abstract algebra