cohesive topos
cohesive (∞,1)-topos
cohesive homotopy type theory
(∞,1)-topos theory
higher geometry
motivation for cohesive toposes
locally connected topos / locally ∞-connected (∞,1)-topos
connected topos / ∞-connected (∞,1)-topos
strongly connected topos / strongly ∞-connected (∞,1)-topos
totally connected topos / totally ∞-connected (∞,1)-topos
local topos / local (∞,1)-topos.
cohesive topos / cohesive (∞,1)-topos
locally connected site / locally ∞-connected site
connected site / ∞-connected site
strongly connected site / strongly ∞-connected site
totally connected site / totally ∞-connected site
local site / ∞-local site
cohesive site, ∞-cohesive site
structures in a cohesive (∞,1)-topos
. concrete objects
. cohesive ∞-groups
. cohomology and principal ∞-bundles
. concordance
. geometric homotopy and Galois theory
. van Kampen theorem
. paths and geometric Postnikov towers
. universal coverings and geometric Whitehead towers
. flat ∞-connections and local systems
. de Rham cohomology
. ∞-Lie algebras
. Maurer-Cartan forms and curvature characteristic forms
. differential cohomology
. Chern-Weil homomorphism and ∞-connections
. higher holonomy and Chern-Simons functional
infinitesimal cohesion
. de Rham space
formal cohesive ∞-groupoid
. de Rham theorem
discrete ∞-groupoid
Euclidean-topological ∞-groupoid
smooth ∞-groupoid
synthetic differential ∞-groupoid
super ∞-groupoid
smooth super ∞-groupoid
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Entries discussing aspects of cohesion include the following
motivation for cohesion, geometry of physics
cohesive (∞,1)-topos, cohesive homotopy type theory,
∞-cohesive site
differential cohesion
cohesion
(shape modality ⊣ flat modality ⊣ sharp modality)
(ʃ⊣♭⊣♯)
discrete object, codiscrete object, concrete object
structures in cohesion
(reduction modality ⊣ infinitesimal shape modality ⊣ infinitesimal flat modality)
(Red⊣ʃ inf⊣♭ inf)
reduced object, coreduced object, formally smooth object
formally étale map
structures in differential cohesion
Examples
discrete cohesion
continuous cohesions
smooth cohesion
supergeometric cohesion