About: Dagger compact category

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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). 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, for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics.

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rdfs:label	Dagger compact category (en)
rdfs:comment	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). 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, for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics. (en)
foaf:depiction
dcterms:subject	Monoidal categories Dagger categories
Wikipage page ID	7155145 (xsd:integer)
Wikipage revision ID	1112299963 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Bell state Projective modules Samson Abramsky N-category Monoidal category Basis (linear algebra) Bifunctor Bob Coecke Bra–ket notation Hom-set Dagger category Dagger symmetric monoidal category Quantum computing Monoidal categories Counit Mathematics Natural transformation Closed category Coherence condition Limit (category theory) Linear maps Linear operator Commutative ring Compact closed category Complementarity (physics) Frobenius algebra Functor Span (category theory) Dual object No-cloning theorem No-deleting theorem Tannakian category Finitely generated module Involution (mathematics) Tensor product Coalgebra Cobordism Eigenstate Quantum teleportation Unitary transformation Categorical quantum mechanics Dagger categories Category of relations Category theory Channel-state duality Sergio Doplicher Cosmos (category theory) Category of finite dimensional Hilbert spaces Observable Topological quantum field theory Topological quantum field theories John Baez Opposite (category theory) Matrix transpose Comultiplication Hermitian conjugate Internal hom functor Comonoid object Compact topological group Completely positive Unit (category theory) dbr:Logic_gate_teleportation dbr:Yanking_condition
sameAs	Dagger compact category Dagger compact category Dagger compact category Dagger compact category
dbp:wikiPageUsesTemplate	dbt:Clarify dbt:Improve_lead dbt:Nlab dbt:Reflist dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/Dagger_compact_category_(diagram).png?width=300
date	May 2015 (en)
id	dagger-compact+category (en)
reason	Can this be expressed symbolically? (en) What is the bar in the following equation? (en)
title	Dagger-compact category (en)
has abstract	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). 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, for n = 1 and k = 3. They are a fundamental structure in Samson Abramsky and Bob Coecke's categorical quantum mechanics. (en)
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page length (characters) of wiki page	15238 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Dagger_compact_category
is Link from a Wikipage to another Wikipage of	Monoidal category Bob Coecke Dagger category

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