Search results for " 18D05"

showing 3 items of 3 documents

On operads, bimodules and analytic functors

2017

We develop further the theory of operads and analytic functors. In particular, we introduce a bicategory that has operads as 0-cells, operad bimodules as 1-cells and operad bimodule maps as 2-cells, and prove that this bicategory is cartesian closed. In order to obtain this result, we extend the theory of distributors and the formal theory of monads.

General Mathematics0102 computer and information sciences01 natural sciencesMathematics::Algebraic TopologyQuantitative Biology::Cell BehaviorMathematics::K-Theory and HomologyMathematics::Quantum AlgebraMathematics::Category Theory18D50 55P48 18D05 18C15FOS: MathematicsAlgebraic Topology (math.AT)Category Theory (math.CT)Mathematics - Algebraic Topology0101 mathematicsMathematicsFunctorOperad bimodule analytic functor bicategoryTheoryMathematics::Operator AlgebrasApplied Mathematics010102 general mathematicsOrder (ring theory)Mathematics - Category Theory16. Peace & justiceBicategoryAlgebraCartesian closed category010201 computation theory & mathematicsBimodule
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Bipullbacks of fractions and the snail lemma

2017

Abstract We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a π 0 - π 1 exact sequence associated with a fractor between groupoids internal to a pointed exact category.

Pure mathematicsLemma (mathematics)Exact sequenceInternal groupoidAlgebra and Number Theory010102 general mathematicsMathematics - Category TheoryBicategory of fraction18B40 18D05 18E35 18G5001 natural sciencesMathematics::Algebraic TopologySettore MAT/02 - AlgebraExact categoryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFOS: MathematicsBipullbackSnail lemmaCategory Theory (math.CT)010307 mathematical physics0101 mathematicsMathematics
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Polynomial functors and polynomial monads

2009

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

Pure mathematicsPolynomialFunctorGeneral MathematicsMathematics - Category Theory18C15 18D05 18D50 03G30517 - AnàlisiMonad (functional programming)BicategoryMathematics::Algebraic TopologyCartesian closed categoryMathematics::K-Theory and HomologyMathematics::Category TheoryPolynomial functor polynomial monad locally cartesian closed categories W-types operadsFOS: MathematicsPolinomisCategory Theory (math.CT)Mathematics
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