nLab
reflective product-preserving sub-(∞,1)-category - internal formulation
Contents
Context
Notions of subcategory
-topos theory
(∞,1)-topos theory
Background
Definitions
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elementary (∞,1)-topos
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(∞,1)-site
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reflective sub-(∞,1)-category
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(∞,1)-category of (∞,1)-sheaves
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(∞,1)-topos
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(n,1)-topos, n-topos
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(∞,1)-quasitopos
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(∞,2)-topos
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(∞,n)-topos
Characterization
Morphisms
Extra stuff, structure and property
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hypercomplete (∞,1)-topos
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over-(∞,1)-topos
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n-localic (∞,1)-topos
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locally n-connected (n,1)-topos
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structured (∞,1)-topos
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locally ∞-connected (∞,1)-topos, ∞-connected (∞,1)-topos
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local (∞,1)-topos
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cohesive (∞,1)-topos
Models
Constructions
structures in a cohesive (∞,1)-topos
Contents
Idea
The external definition of reflective sub-(∞,1)-category via the universal property of the reflector has an immediate formulation in the internal language of an (∞,1)-topos. This internal formulation, however, automatically gives a reflective product-preserving sub-(∞,1)-category.
References
HoTT-Coq code for internal reflective subcategories is at
The fact that in the internal formulation reflective subcategories are automatically product-preserving is mentioned on p. 5 of
Last revised on November 21, 2011 at 16:40:57.
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