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16,092
in monoidal categories
, 1995
"... We consider the theory of operads and their algebras in enriched category theory. We introduce the notion of simplicial A~cgraph and show that some important constructions of homotopy coherent category theory lead by a natural way to the use of such objects as the appropriate homotopy coherent coun ..."
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We consider the theory of operads and their algebras in enriched category theory. We introduce the notion of simplicial A~cgraph and show that some important constructions of homotopy coherent category theory lead by a natural way to the use of such objects as the appropriate homotopy coherent
Cohomology of Monoids in Monoidal Categories
 In &quot;Operads: Proceedings of renaissance conferences.&quot; Contemp. Math. 202, AMS
, 1997
"... this article we show that these structures are still susceptible to cohomological investigation, by developing the theory in the absence of the symmetry condition. Later we shall assume that the monoidal structure is left distributive over coproducts and the category is an abelian category; this is ..."
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Cited by 8 (2 self)
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this article we show that these structures are still susceptible to cohomological investigation, by developing the theory in the absence of the symmetry condition. Later we shall assume that the monoidal structure is left distributive over coproducts and the category is an abelian category
Graded extensions of monoidal categories
 J. ALGEBRA
, 2001
"... The longknown results of SchreierEilenbergMac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application is mad ..."
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Cited by 6 (3 self)
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The longknown results of SchreierEilenbergMac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application
CORINGS IN MONOIDAL CATEGORIES
"... Following methods of Pareigis and Schauenburg we study corings in monoidal categories and their categories of representations. In particular, we pay attention to the case where the ..."
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Following methods of Pareigis and Schauenburg we study corings in monoidal categories and their categories of representations. In particular, we pay attention to the case where the
Involutive monoidal categories
, 2010
"... Abstract. In this paper, we consider a nonposetal analogue of the notion of involutive quantale [MP92]; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring. We study the coherence issues that inevitably result when passing from posets ..."
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Cited by 5 (0 self)
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Abstract. In this paper, we consider a nonposetal analogue of the notion of involutive quantale [MP92]; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring. We study the coherence issues that inevitably result when passing from
DESCENT IN MONOIDAL CATEGORIES
"... Abstract. We consider a symmetric monoidal closed category V = (V, ⊗, I, [−, −]) together with a regular injective object Q such that the functor [−, Q]: V → V op is comonadic and prove that in such a category, as in the monoidal category of abelian groups, a morphism of commutative monoids is an ef ..."
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Abstract. We consider a symmetric monoidal closed category V = (V, ⊗, I, [−, −]) together with a regular injective object Q such that the functor [−, Q]: V → V op is comonadic and prove that in such a category, as in the monoidal category of abelian groups, a morphism of commutative monoids
Coherence for SkewMonoidal Categories
"... I motivate a variation (due to K. Szlachányi) of monoidal categories called skewmonoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the wellknown monoidal case. In my (to ..."
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Cited by 1 (0 self)
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I motivate a variation (due to K. Szlachányi) of monoidal categories called skewmonoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the wellknown monoidal case. In my
Entwining Structures in Monoidal Categories
 J. Algebra
"... Abstract. Interpreting entwining structures as special instances of J. Beck’s distributive law, the concept of entwining module can be generalized for the setting of arbitrary monoidal category. In this paper, we use the distributive law formalism to extend in this setting basic properties of entwin ..."
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Cited by 12 (7 self)
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Abstract. Interpreting entwining structures as special instances of J. Beck’s distributive law, the concept of entwining module can be generalized for the setting of arbitrary monoidal category. In this paper, we use the distributive law formalism to extend in this setting basic properties
MONOIDAL CATEGORIES OF CORINGS
, 2004
"... Abstract. We introduce a monoidal category of corings using two different notions of corings morphisms. The first one is the (right) coring extensions recently introduced by T. Brzeziński in [2], and the anther is the usual notion of morphisms defined in [5] by J. GómezTorrecillas. ..."
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Abstract. We introduce a monoidal category of corings using two different notions of corings morphisms. The first one is the (right) coring extensions recently introduced by T. Brzeziński in [2], and the anther is the usual notion of morphisms defined in [5] by J. GómezTorrecillas.
Results 1  10
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16,092