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String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another.
Mathematische Grundlagen der Quantenmechanik
J. von Neumann · 1932
Earlier work this paper cites.
On adding relations to homotopy groups
J. H. C. Whitehead · 1941
Earlier work this paper cites.
Von Neumann and lattice theory
G. Birkhoff · 1958
Earlier work this paper cites.
Group-like structures in general categories I: multiplications and comultiplications
B. Eckmann and P. J. Hilton · 1962
Earlier work this paper cites.
Functorial Semantics of algebraic theories
F.W. Lawvere · 1963
Earlier work this paper cites.
Natural associativity and commutativity
S. Mac Lane · 1963
Earlier work this paper cites.
Badly incomplete normed linear spaces
A.H. Kruse · 1964
Earlier work this paper cites.
Application of dual-number quaternion algebra to the analysis of spatial mechanisms
A.T. Yang and F. Freudenstein · 1964
Earlier work this paper cites.
Closed categories
S. Eilenberg and G.M. Kelly · 1966
Earlier work this paper cites.
Introduction to bicategories
J. Bénabou · 1967
Earlier work this paper cites.
Homotopical Algebra
D.G. Quillen · 1967
Earlier work this paper cites.
Distributive laws
J. Beck · 1969
Earlier work this paper cites.
The Topology of CW Complexes
A.T. Lundell and S. Weingram · 1969
Earlier work this paper cites.
On closed categories of functors
B. Day · 1970
Earlier work this paper cites.
H-spaces from a Homotopy Point of View
J. Stasheff · 1970
Earlier work this paper cites.
Applications of negative dimensional tensors
R. Penrose · 1971
Earlier work this paper cites.
Many-variable functorial calculus. I
G.M. Kelly · 1972
Earlier work this paper cites.
Homotopy invariant algebraic structures on topological spaces
J. M. Boardman and R. M. Vogt · 1973
Earlier work this paper cites.
Topology and logic as a source of algebra
S. Mac Lane · 1976
Earlier work this paper cites.
Limits indexed by category-valued 2-functors
R. Street · 1976
Earlier work this paper cites.
Yoneda structures on 2-categories
R. Street and R. Walters · 1978
Earlier work this paper cites.
Communication by EPR devices
D. Dieks · 1982
Earlier work this paper cites.
A single quantum cannot be cloned
W. K. Wootters and W. H. Zurek · 1982
Earlier work this paper cites.
On lexicographically shellable posets
A. Björner and M.L. Wachs · 1983
Earlier work this paper cites.
The Lambda Calculus: Its Syntax and Semantics
H. P. Barendregt · 1984
Earlier work this paper cites.
Posets, regular CW complexes and Bruhat order
A. Björner · 1984
Earlier work this paper cites.
The algebra of oriented simplexes
R. Street · 1987
Earlier work this paper cites.
The combinatorics of n-categorical pasting
M. Johnson · 1989
Earlier work this paper cites.
Bell’s theorem without inequalities
D.M. Greenberger, M.A. Horne, A. Shimony, and A. Zeilinger · 1990
Earlier work this paper cites.
Matrices, relations, and group representations
A. Carboni · 1991
Earlier work this paper cites.
Quantum cryptography based on Bell’s theorem
A.K. Ekert · 1991
Earlier work this paper cites.
The geometry of tensor calculus, I
A. Joyal and R. Street · 1991
Earlier work this paper cites.
Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results)
M. M. Kapranov and V. A. Voevodsky · 1991
Earlier work this paper cites.
∞ \infty -groupoids and homotopy types
M.M. Kapranov and V.A. Voevodsky · 1991
Earlier work this paper cites.
An n-categorical pasting theorem
A.J. Power · 1991
Earlier work this paper cites.
Parity complexes
R. Street · 1991
Earlier work this paper cites.
Categories of space and of quantity
F.W. Lawvere · 1992
Earlier work this paper cites.
Higher-dimensional word problems with applications to equational logic
A. Burroni · 1993
Earlier work this paper cites.
The algebra of directed complexes
R. Steiner · 1993
Earlier work this paper cites.
Fock space: A model of linear exponential types. Corrected version of Holomorphic models of exponential types in linear logic
R. Blute, P. Panangaden, and R. Seely · 1994
Earlier work this paper cites.
2-categories and Zamolodchikov tetrahedra equations, 1994
M.M. Kapranov and V.A. Voevodsky · 1994
Earlier work this paper cites.
Nonsymmetric
M. Barr · 1995
Earlier work this paper cites.
Pasting schemes for the monoidal biclosed structure on ω \omega -Cat
S. E. Crans · 1995
Earlier work this paper cites.
Proof-nets and the Hilbert space
V. Danos and L. Regnier · 1995
Earlier work this paper cites.
Noncommuting mixed states cannot be broadcast
H. Barnum, C.M. Caves, C.A. Fuchs, R. Jozsa, and B. Schumacher · 1996
Earlier work this paper cites.
Natural deduction and coherence for weakly distributive categories
R.F. Blute, J.R.B. Cockett, R.A.G. Seely, and T.H. Trimble · 1996
Earlier work this paper cites.
Proof-nets: the parallel syntax for proof-theory
J.-Y. Girard · 1996
Earlier work this paper cites.
Weakly distributive categories
J.R.B. Cockett and R.A.G. Seely · 1997
Earlier work this paper cites.
Presentations of omega-categories by directed complexes
S.E. Crans and R. Steiner · 1997
Earlier work this paper cites.
Stabilizer Codes and Quantum Error Correction
D. Gottesman · 1997
Earlier work this paper cites.
Disks, duality and
A. Joyal · 1997
Earlier work this paper cites.
Computads for finitary monads on globular sets
M.A. Batanin · 1998
Earlier work this paper cites.
Monoidal globular categories as a natural environment for the theory of weak n-categories
M.A. Batanin · 1998
Earlier work this paper cites.
Categorification, 1998
J.C. Baez and J. Dolan · 1998
Earlier work this paper cites.
Higher-dimensional algebra III. n-categories and the algebra of opetopes
J.C. Baez and J. Dolan · 1998
Earlier work this paper cites.
A concise course in algebraic topology
J. P. May · 1999
Earlier work this paper cites.
Introduction to linear bicategories
J.R.B. Cockett, J. Koslowski, and R.A.G. Seely · 2000
Earlier work this paper cites.
Three qubits can be entangled in two inequivalent ways
W. Dür, G. Vidal, and J.I. Cirac · 2000
Earlier work this paper cites.
Representable multicategories
C. Hermida · 2000
Earlier work this paper cites.
Impossibility of deleting an unknown quantum state
A.K. Pati and S.L. Braunstein · 2000
Earlier work this paper cites.
Persistent entanglement in arrays of interacting particles
H.J. Briegel and R. Raussendorf · 2001
Earlier work this paper cites.
From coherent structures to universal properties
C. Hermida · 2001
Earlier work this paper cites.
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L.H. Kauffman · 2001
Earlier work this paper cites.
Duality for simple
M. Makkai and M. Zawadowski · 2001
Earlier work this paper cites.
Multiple categories: the equivalence of a globular and a cubical approach
F. A. Al-Agl, R. Brown, and R. Steiner · 2002
Earlier work this paper cites.
A cellular nerve for higher categories
C. Berger · 2002
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S.B. Bravyi and A.Y. Kitaev · 2002
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