This article's lead section may be too short to adequately summarize the key points. Please consider expanding the lead to provide an accessible overview of all important aspects of the article.(January 2016)
In category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio Doplicher and John E. Roberts on the reconstruction of compact topological groups from their category of finite-dimensional continuous unitary representations (that is, Tannakian categories).[1] They also appeared in the work of John Baez and James Dolan as an instance of semistrict k-tuply monoidal n-categories, which describe general topological quantum field theories,[2] for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics.[3][4][5]
^Doplicher, S.; Roberts, J. (1989). "A new duality theory for compact groups". Invent. Math. 98: 157–218. Bibcode:1989InMat..98..157D. doi:10.1007/BF01388849. S2CID 120280418.
^Baez, J.C.; Dolan, J. (1995). "Higher-dimensional Algebra and Topological Quantum Field Theory". J. Math. Phys. 36 (11): 6073–6105. arXiv:q-alg/9503002. Bibcode:1995JMP....36.6073B. CiteSeerX 10.1.1.269.4681. doi:10.1063/1.531236. S2CID 14908618.
^Abramsky, S.; Coecke, B. (2004). "A categorical semantics of quantum protocols". Proceedings of the 19th IEEE conference on Logic in Computer Science (LiCS'04). IEEE. pp. 415–425. arXiv:quant-ph/0402130. CiteSeerX 10.1.1.330.7289. doi:10.1109/LICS.2004.1319636. ISBN 0-7695-2192-4. S2CID 1980118.
^Abramsky, S.; Coecke, B. (2009). "Categorical quantum mechanics". In Engesser, K.; Gabbay, D.M.; Lehmann, D. (eds.). Handbook of Quantum Logic and Quantum Structures. Elsevier. pp. 261–323. arXiv:0808.1023. ISBN 978-0-08-093166-1.
^Abramsky and Coecke used the term strongly compact closed categories, since a dagger compact category is a compact closed category augmented with a covariant involutive monoidal endofunctor.
and 24 Related for: Dagger compact category information
In category theory, a branch of mathematics, daggercompactcategories (or daggercompact closed categories) first appeared in 1989 in the work of Sergio...
In category theory, a branch of mathematics, a daggercategory (also called involutive category or category with involution) is a category equipped with...
In category theory, a branch of mathematics, compact closed categories are a general context for treating dual objects. The idea of a dual object generalizes...
between dagger categories and the daggercompactcategories that are used in categorical quantum mechanics, an area that now also considers dagger symmetric...
the daggercompactcategories. Tannakian categories are monoidal categories enriched over a field, which are very similar to representation categories of...
a closed category, and furthermore a daggercompactcategory. The category Rel can be obtained from the category Set as the Kleisli category for the monad...
algebra. The stable category of a Frobenius category is canonically a triangulated category. Daggercompactcategory Tannakian category Theorem 2.6 in Happel...
A dagger is a fighting knife with a very sharp point and usually one or two sharp edges, typically designed or capable of being used as a cutting or thrusting...
the teleportation protocol can be written mathematically. Some are very compact but abstract, and some are verbose but straightforward and concrete. The...
A push dagger (alternately known as a punch dagger, punch knife, push knife or, less often, a push dirk) is a short-bladed dagger with a "T" handle designed...
The category is a daggercompactcategory. A topological quantum field theory is a monoidal functor from a category of cobordisms to a category of vector...
Mathematics portal Biography portal Algebraic quantum field theory Daggercompactcategory Gauge group Local quantum physics Noncommutative quantum field...
The Napier Dagger was a 24-cylinder H-pattern (or H-Block) air-cooled engine designed by Frank Halford and built by Napier before World War II. It was...
The Legazpi-Sikatuna Blood Compact or Sandugo (Spanish: Pacto de Sangre) was a blood compact, performed in the island of Bohol in the Philippines, between...
(Obsolete) attribute on br element compact attribute on dl, dir and menu elements type (Deprecated. use CSS instead.), compact (Deprecated. use CSS instead...
electrical line during a battle in Iraq A Gerber Compact Sport 400 multitool, closed A Gerber Compact Sport 400 multitool, open A Gerber Mark II combat...
functions on a compact interval, with the uniform convergence norm), have denumerable (i. e. countably infinite) dimension in the category of Banach spaces...
This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...
received Certificate of Merit: The double-dagger (‡) indicates Short Drama or Multi-episodes Documentary The dagger (†) indicates Single-episode Drama Serial...
Global Information