∞-Categories for the Working Mathematician

By Emily Riehl, Dominic R. Verity. 2018

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Citations in the corpus

Causality for Machine Learning (2019, background): “3 The intriguing idea of starting from symmetry transformations and defining objects by their behavior under these transformations has been fruitful not just in physics but also in mathematics (Klein, 1872; MacLane, 1971).”
Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory (2015, background): “That is, Dop is the twisted arrow category [57,4] of Δ.”
Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures (2016, background): “The same applies to the monad for direct sums or biproducts (in the terminology of [41]).”
Foundations of Rigid Geometry I (2013, background): “In this book, categories are always considered within set theory; our standard reference to category theory is [68].”
Higher Segal Spaces (2012, unknown): “More generally, one can define the geometric realization of any simplicial space X ∈ Top∆ by gluing the spaces Xn × ∣∆n∣ or, more precisely, forming the coend (see [ML98]) of the bivariant functor X● × ∣∆●∣ ∶∆op ×∆Ð→ Top, ([m], [n]) ↦Xm × ∣∆n∣.”
Tensor categories (2023, background): “For deﬁnitions and basic facts of category theory, such as adjoint functors, limits, ends see [Mac Lane (1971)].”
Operads, algebras, modules and motives (2018, background): “The standard coherence isomorphisms (= associativity and commutativity constraints) on the tensor product pass to the derived category, which is thus a symmetric monoidal closed category in the sense of [43, 36].”
A mathematical theory of resources (2014, unknown): “By Mac Lane’s strictiﬁcation theorem [35, p.257], any (non-strict) monoidal category is equivalent (via a pair of strong monoidal functors) to a strict one.”