Higher Topos Theory

Lurie, J. (2009). Higher Topos Theory. Princeton University Press.

Type

Book

Intellectual base

Review or monograph

Year

2009

DOI

10.1515/9781400830558

ISBN

9781400830558

DOI registrant

Princeton University Press

Link

https://doi.org/10.1515/9781400830558

Cited by

8 citations across 8 artifacts.

Domain-specific

• Accessible quasi-category
  • Accessibility is relative to some regular cardinal, accessible infinity-categories are typically large, small accessible cases are highly restricted and presentability adds existence of all small colimits.
• Diamond Operation
  • Equivalently, it is the pushout \(X\diamond Y=(X\times Y\times\Delta^1)\amalg_{X\times Y\times\partial\Delta^1}(X\amalg Y)\), with the endpoint maps understood as those projections.
• Join (simplicial sets)
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Joyal Model Structure
  • Fibrations are then the maps having the right lifting property against the trivial cofibrations; terminology such as categorical fibration, isofibration, or pseudo-fibration must be tied to the source's exact convention.
• Opposite simplicial set
  • Opposition reverses simplex orientation coherently in every dimension rather than merely reversing individual one-dimensional arrows.
• Presheaf (category theory)
  • … canonical instance directly demonstrates that the base category, target category, object assignment, contravariant morphism assignment and functor identity and composition laws are explicit. to An applied instance preserves the same invariant under a changed scale, notation, jurisdiction, dataset, or implementation..
• Simplicially enriched category
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Topological category (enriched category theory)
  • A topological category is a category enriched in topological spaces: each hom-object is a space and composition and units are morphisms in the enriching topological category.

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://www.math.ias.edu/~lurie/papers/HTT2012.pdf ×1

Registry ID ref:7a3ea91807fa · see in the full table