Homotopical inverse diagrams in categories with attributes

@article{Kapulkin2018HomotopicalID,
  title={Homotopical inverse diagrams in categories with attributes},
  author={Chris Kapulkin and Peter LeFanu Lumsdaine},
  journal={arXiv: Logic},
  year={2018}
}
We define and develop the infrastructure of homotopical inverse diagrams in categories with attributes (CwA's). Specifically, given a category with attributes C and an ordered homotopical inverse category I, we construct the category with attributes C^I of homotopical diagrams of shape I in C and Reedy types over these, and we show how various logical structure (Pi-types, identity types, and so on) lifts from the original CwA to the diagram CwA. This may be seen as providing a general class… 
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