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Symmetric monoidal categories and graphical reasoning 29

RELATIVE SYMMETRIC MONOIDAL CLOSED CATEGORIES I:

RELATIVE SYMMETRIC MONOIDAL CLOSED CATEGORIES I:

... Abstract. Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to ...each ...

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Hopf Cyclic Cohomology in Non symmetric Monoidal Categories

Hopf Cyclic Cohomology in Non symmetric Monoidal Categories

... 2 American University of Middle East (in affiliation with Purdue University), Kuwait Copyright c ⃝ 2015 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of ...

7

CiteSeerX — Finite dimensional vector spaces are complete for traced symmetric monoidal categories

CiteSeerX — Finite dimensional vector spaces are complete for traced symmetric monoidal categories

... traced symmetric monoidal categories via interpretations in the very familiar setting of linear algebra: the category FinVect k of finite dimensional vector spaces and linear maps over a field ...

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2. Indexed monoidal categories

2. Indexed monoidal categories

... indexed symmetric monoidal categories. An indexed symmetric monoidal category is a family of symmetric monoidal categories C A , one for each object A of a ...

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THE LINEARITY OF TRACES IN MONOIDAL CATEGORIES AND BICATEGORIES

THE LINEARITY OF TRACES IN MONOIDAL CATEGORIES AND BICATEGORIES

... IN MONOIDAL CATEGORIES AND BICATEGORIES KATE PONTO AND MICHAEL SHULMAN ...any symmetric monoidal category, if a weight for colim- its is absolute, then the resulting colimit of any diagram of ...

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Rewriting modulo symmetric monoidal structure

Rewriting modulo symmetric monoidal structure

... Lawvere categories [19], the corresponding (linear 2 ) notion for SMTs is the one of PROP [28] (product and permutation ...a symmetric strict monoidal category with objects the natural numbers, where ...

10

CiteSeerX — Closed symmetric monoidal structure and flow

CiteSeerX — Closed symmetric monoidal structure and flow

... Proposition 5.2) since the path space P(X ⊗Y ) is exactly (PX ×Y 0 )⊔(X 0 ×PY )⊔(PX ×PY ) with the composition law that one expects to find. And it turns out that this new symmetric monoidal structure is ...

14

A graphical calculus for shifted symmetric functions

A graphical calculus for shifted symmetric functions

... 1.5 Khovanov’s Heisenberg category We define a C -linear strict monoidal category H 1 generated by two objects Q and Q as follows. An object of H 1 is a finite direct sum of tensor products Q 1 b b Q m , where 1 , ...

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Yang–Baxter operators in symmetric categories

Yang–Baxter operators in symmetric categories

... arbitrary symmetric monoidal category C , we call a pair (X, r) consisting of a cocommutative coalgebra in C and a non-degenerate solution, a non-degenerate braided ...tensor categories; we prove ...

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Symmetric powers in abstract homotopy categories

Symmetric powers in abstract homotopy categories

... out symmetric powers ( Theorem 22 ...then symmetric powers preserve weak equivalences between cofibrant objects and so admit their left derived endofunctors on C ( Theorem 25 ...generated monoidal ...

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Distributive laws for actions of monoidal categories arxiv:math/ v2 [math.ct] 14 Jul 2004

Distributive laws for actions of monoidal categories arxiv:math/ v2 [math.ct] 14 Jul 2004

... 3 The crucial point missing from 2a-c, and from the bulk of recorded “noncommutative” literature is failing to adhere to the old Grothendieck’s advice that geometrical study of morphisms (hence actions in particular) ...

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2. Background on monoidal bicategories

2. Background on monoidal bicategories

... of categories weakly enriched in a monoidal bicategory using a notion of enriched icon as ...the monoidal bicategory in question is symmetric then this process can be ...the symmetric ...

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Ligon, Thomas S.
  

(1978):


	Galois theory in monoidal categories.


Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

Ligon, Thomas S. (1978): Galois theory in monoidal categories. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

... 11, categories of topological vector spaces are investigated to see how many interesting examples of “finite” objects in the sense of Definition ...these categories is symmetric and closed ...

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3. Monoidal biclosed structures on 2-Cat

3. Monoidal biclosed structures on 2-Cat

... No monoidal model structure. The cartesian product of categories and Gray tensor product of 2-categories are generally considered to be homotopically well behaved tensor ...of categories is ...

24

Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures

Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures

... small categories and its hom-categories are given by CatSym [X, Y] = def S -Prof [Y, X] = CAT [ S (X) op × Y, Set ] ...categorical symmetric sequences F : X → Y and G : Y → Z , ...categorical ...

40

Operads in Iterated Monoidal Categories

Operads in Iterated Monoidal Categories

... The fact that monoids are single object enriched categories also leads to an efficient expanded definition of m-fold operads in an n-fold monoidal category.. Let V be an n-fold monoidal [r] ...

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2. Weak braided monoidal categories

2. Weak braided monoidal categories

... Braided monoidal categories have been much studied and are used extensively in many areas of mathematics, for instance in knot theory, representation theory and topological quantum field ...braided ...

10

CiteSeerX — Additive closed symmetric monoidal structures on R-modules

CiteSeerX — Additive closed symmetric monoidal structures on R-modules

... Further calculation with this last equation yields b 1 Λ = u −1 b 1 Γ . This means that if b 1 Γ is nonzero, we can choose u so as to ensure b 1 Λ = 1. Said another way, given Γ with b 1 nonzero, we can define Λ = R u −1 ...

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BRAIDED SKEW MONOIDAL CATEGORIES JOHN BOURKE AND STEPHEN LACK Abstract

BRAIDED SKEW MONOIDAL CATEGORIES JOHN BOURKE AND STEPHEN LACK Abstract

... Given a monoidal comonad G, in addition to the cowarped skew monoidal category C[G], we can form the lifted monoidal structure on the Eilenberg-Moore category C G of coalgebras... BRAIDE[r] ...

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SZX-Calculus: Scalable Graphical Quantum Reasoning

SZX-Calculus: Scalable Graphical Quantum Reasoning

... Contributions. We introduce the Scalable ZX-calculus, SZX calculus for short, to provide theoretical foundations to this approach. We extend the ZX-calculus to deal with registers of qubits by introducing some new ...

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