A multicategorical approach to mixed linear-non-linear substitution – Christine Tasson

Christine Tasson
LIP6, Sorbonne Université

Date(s) : 26/11/2020   iCal
11 h 00 min - 12 h 30 min

I will present a colimit construction of 2-monad that we studied with Martin Hyland with the purpose of understanding the mixed linear-non-linear framework at play in differential lambda-calculus. Differentiation that appears in standard calculus, differential lambda-calculus and differential categories, is an operator that transforms a function A -> B into its best linear approximation, that is a function AxA->B where the first parameter is linear. Therefore,
we have two kinds of composition/substitution that live together. In order to better understand this framework, we use the multicategorical framework with a monadic presentation. Both the linear and the non-linear setting can be understood through a 2-monad, and our colimit construction allows to build the mixed linear-non-linear


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