A tribe, or type-theoretic fibration category, is a version of a fibration category that is adapted to describe the categorical semantics of dependent type theory and in particular homotopy type theory
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Michael Shulman, Univalence for inverse diagrams and homotopy canonicity, Mathematical Structures in Computer Science, Volume 25, Issue 5 ( From type theory and homotopy theory to Univalent Foundations of Mathematics ) June 2015 (arXiv:1203.3253, doi:/10.1017/S0960129514000565)
André Joyal, What is categorical type theory, various talks in 2013, (pdf)
André Joyal, Notes on Clans and Tribes, arxiv:1710.10238
Chris Kapulkin and Karol Szumilo, Internal Language of Finitely Complete (∞,1)-categories, arxiv:1709.09519
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