nLab
internal infinity-categories contents

category object in an (∞,1)-category, groupoid object

In a 1-category

• Bishop set, setoid

• internal category, internal groupoid

  weak equivalence of internal categories

• internal functor, internal profunctor

• internal diagram, internal presheaf

• n-fold category, cat-n-group

In a (2,1)-category

• 2-congruence

In ∞Grpd

• semi-Segal space, Segal space, complete Segal space,

• reduced Segal space

In $\mathrm{Cat}(\mathrm{Cat}(\cdots \mathrm{Cat}(\mathrm{\infty }\mathrm{Grpd})))$

• higher Segal space

• n-fold complete Segal space

• Theta space

In (n,r)-categories

• (n,r)-congruence

Model category presentations

• model structure for complete Segal spaces

Internal $n$-category

• n-category object in an (∞,1)-category

• Theta_n space

Operadic case

• model structure for dendroidal complete Segal spaces

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