Results 11 - 20
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42
Functorial calculus in monoidal bicategories
- Applied Categorial Structures
, 2002
"... The definition and calculus of extraordinary natural transformations [EK] is extended to a context internal to any autonomous monoidal bicategory [DyS]. The original calculus is recaptured from the geometry [SV], [MT] of the monoidal bicategory V-Mod whose objects are categories enriched in a cocomp ..."
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Cited by 5 (1 self)
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The definition and calculus of extraordinary natural transformations [EK] is extended to a context internal to any autonomous monoidal bicategory [DyS]. The original calculus is recaptured from the geometry [SV], [MT] of the monoidal bicategory V-Mod whose objects are categories enriched in a cocomplete symmetric monoidal
Rational combinatorics
"... We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials. ..."
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Cited by 5 (4 self)
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We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.
p-Form Electromagnetism on Discrete Spacetimes
, 2006
"... We investigate p-form electromagnetism—with the Maxwell and Kalb-Ramond fields as lowest-order cases—on discrete spacetimes, including the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitab ..."
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Cited by 5 (1 self)
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We investigate p-form electromagnetism—with the Maxwell and Kalb-Ramond fields as lowest-order cases—on discrete spacetimes, including the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitable for our purpose—a chain complex equipped with an inner product on (p + 1)-cochains—we study both the classical and quantum versions of the theory, with either R or U(1) as gauge group. We find results—such as a ‘p-form Bohm–Aharonov effect’—that depend in interesting ways on the cohomology of spacetime. We quantize the theory via the Euclidean path integral formalism, where the natural kernels in the U(1) theory are not Gaussians but theta functions. As a special case of the general theory, we show p-form electromagnetism in p + 1 dimensions has an exact solution which reduces when p = 1 to the abelian case of 2d Yang-Mills theory as studied by Migdal and Witten. Our main result describes p-form electromagnetism as a ‘chain field theory’—a theory analogous to a topological quantum field theory, but with chain complexes replacing manifolds. This makes precise a notion of time evolution in the context of discrete spacetimes of arbitrary topology.
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
- Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about well-behaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Cited by 4 (1 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about well-behaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOS-like specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
Homotopy operations and rational homotopy type”, in Algebraic Topology: Categorical decomposition techniques
- Prog. in Math. 215, Birkhäuser, Boston-Basel
"... In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection ..."
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Cited by 4 (4 self)
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In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection
A general theory of self-similarity II: recognition, e-print math.DS/0411345
"... www.maths.gla.ac.uk/∼tl ..."
Super, Quantum and Non-Commutative Species
, 2009
"... Dedicated to the memory of Gian-Carlo Rota. We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual dual ..."
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Cited by 3 (3 self)
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Dedicated to the memory of Gian-Carlo Rota. We introduce an approach to the categorification of rings, via the notion of distributive categories with negative objects, and use it to lay down categorical foundations for the study of super, quantum and non-commutative combinatorics. Via the usual duality between algebra and geometry, these constructions provide categorifications for various types of affine spaces, thus our works may be regarded as a starting point towards the construction of a categorical geometry.
Lattice p-form electromagnetism and chain field theory
- LOOPS ’05, ALBERT EINSTEIN INSTITUT, MAX PLANCK GESELLSCHAFT, GOLM
, 2005
"... Since Wilson’s work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in str ..."
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Cited by 2 (2 self)
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Since Wilson’s work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such ‘higher gauge theories ’ in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a ‘chain field theory’ — a theory analogous to topological quantum field theory, but with chain complexes replacing
2007a), Components, Complements and the Reflection Formula, Theory and
"... ABSTRACT. Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (↓P)x = ten(x/X, P) ; (P↓)x = hom(X/x, P) ..."
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Cited by 2 (2 self)
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ABSTRACT. Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (↓P)x = ten(x/X, P) ; (P↓)x = hom(X/x, P)
Pullback and finite coproduct preserving functors between categories of permutation representations, Theory and Applications of Categories 16
, 2006
"... Abstract. Francisco Marmolejo pointed out a mistake in the statement of Proposition 4.4 in our paper [PS]. The mistaken version is used later in that paper. Our purpose here is to correct the error by providing an explicit description of the finite coproduct ..."
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Cited by 1 (1 self)
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Abstract. Francisco Marmolejo pointed out a mistake in the statement of Proposition 4.4 in our paper [PS]. The mistaken version is used later in that paper. Our purpose here is to correct the error by providing an explicit description of the finite coproduct

