# Kan Extensions are Partial Colimits

@article{Perrone2022KanEA, title={Kan Extensions are Partial Colimits}, author={Paolo Perrone and Walter Tholen}, journal={Applied Categorical Structures}, year={2022} }

One way of interpreting a left Kan extension is as taking a kind of “partial colimit”, whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the partial evaluations sitting in the so-called bar construction of monads. The (pseudo)monads of interest for forming colimits are the monad of diagrams and the monad of small presheaves, both on the (huge) category CAT of locally small categories. Throughout, particular care is taken to handle size issues…

## 2 Citations

A diagrammatic view of differential equations in physics

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Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put…

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This paper consists of two parts. First, within the framework of Grothendieck's fibrational category theory, we present a certain web of fundamental adjunctions surrounding the category of all small…

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