Search results for " analytic functor"

showing 2 items of 2 documents

The cartesian closed bicategory of generalised species of structures

2007

AbstractThe concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature — including of course Joyal's original notion — together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our secon…

FunctorGeneral MathematicsSubstitution (logic)species of structures analytic functorPresheafComposition (combinatorics)BicategoryMathematics::Algebraic TopologyAlgebraCartesian closed categoryCombinatorial speciesMathematics::Category Theorybicategory cartesian closed categoriesMathematicsJournal of the London Mathematical Society
researchProduct

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
researchProduct