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Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
The relative role of the stellar radiation field, the stellar outflows and the interstellar radiation field (ISRF) in transforming the molecular ejecta into atomic gas was the subject of our ISO LWS and SWS spectroscopy study of 24 evolved stars which span the range from AGB stars to proto-planetary nebulae (PPNs) and PNs. The far-infrared (FIR) atomic fine-structure lines are powerful probes of the warm atomic gas in photodissociation regions (PDRs) and shocks. This paper summarizes and compares the ISO spectroscopy studies of carbon-rich (C-rich) and oxygen-rich (O-rich) evolved stars, published by Fong et al. (2001) and Castro-Carrizo et al. (2001), respectively. We find that photodissociation, not shocks, is responsible for the chemical change from molecular to atomic gas.
We present high-sensitivity near-IR images of a carbon-rich proto-planetary nebula, AFGL 618, obtained with the Infrared Camera and Spectrograph (IRCS) mounted on the 8.2m Subaru Telescope. The deep near-IR images have revealed “bullets” and “horns” extending farther out from the edges of the previously known bipolar nebulosities that consist of dust-scattered star light component and shock-excited line emission component. That these bullets and horns represent the positions from which [Fe II] IR lines arise is strongly suggested from the spatial coincidence between these near-IR microstructures and the optical collimated outflow structure observed by the recent HST/WFPC2 imaging, together with the previous detection of shock-excited, forbidden IR lines of atomic species at those locations. At these positions of the near-IR mincrostructures, we have also discovered CO clumps moving at > 200 km s-1 from our re-analysis of the existing 12CO J = 1 – 0 data obtained with the Berkeley-Illinois-Maryland Association (BIMA) interferometer array. These findings indicate that fast-moving CO clumps seem to be impinging upon the surrounding ambient circumstellar shell, thereby causing shocked emission regions which manifest themselves as the near-IR microstructures at the shock interface. To deepen our understanding of the connection between the near-IR microstructures and the CO outflow structure, we are currently conducting higher resolution observation in CO lines with the BIMA array.