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2-Monads for Differential Calculus

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One approach to algebra from an advanced standpoint is based on Kleisli bicategories. Various flavours of substitution are captured by suitable 2-monads. This point of view has many applications. In this talk based on joint work with Christine Tasson I present an application to the substitutions needed to support the Ehrhard-Regnier differential lambda calculus. For that one needs to combine the free symmetric monoidal category 2-monad with the 2-monad for finite products. Known combinations (via distributive laws, tensor or sum) are of no help. I shall establish the existence of a general colimit construction on 2-monads, which does produce the desired 2-monad

This talk is part of the Category Theory Seminar series.

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