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This directory contains material in the context of homotopy type theory http://ncatlab.org/nlab/show/homotopy+type+theory , the internal language of infinity-toposes http://ncatlab.org/nlab/show/(infinity,1)-topos . The directory "Hott/Coq" contains Coq code http://ncatlab.org/nlab/show/Coq for Martin-Löf type theory http://ncatlab.org/nlab/Martin-Löf+type+theory . that sets up the basic notions of homotopy type theory. The subdirectory "HoTT/Coq/HIT" contains code that sets up higher inductive types http://ncatlab.org/nlab/show/higher+inductive+types. The subdirectory "HoTT/Coq/Cohesion" contains code that sets up the internal language of cohesive infinity-toposes http://ncatlab.org/nlab/show/cohesive+(infinity,1)-topos . You can fork this repository to your own and then be automatically kept up to date on new developments. You can also contribute back into it by sending a pull request. The Coq files contain fancy UTF-8 characters. To input these you have to set up an appropriate input method, see http://coq.inria.fr/cocorico/TeXInputMethodForUnicodeNotations for help on doing so with Emacs and CoqIDE.