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Top Papers in Grothendieck construction

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The Enriched Grothendieck Construction

We define and study opfibrations of $V$-enriched categories when $V$ is an
extensive monoidal category whose unit is terminal and connected. This includes
sets, simplicial sets, categories, or any loc

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Monoidal Grothendieck construction

We lift the standard equivalence between fibrations and indexed categories to
an equivalence between monoidal fibrations and monoidal indexed categories,
namely weak monoidal pseudofunctors to the 2-c

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Monoid extensions and the Grothendieck construction

In category theory circles it is well-known that the Schreier theory of group
extensions can be understood in terms of the Grothendieck construction on
indexed categories. However, it is seldom discus

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The Sigma-type motivate isomorphisms in category theory

From the Sigma-type to the Grothendieck construction

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A Monoidal Lift of the Groteck Construction for Network Construction

The Grothendieck Construction in Categorical Network Theory

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2-Cartesian fibrations II: The Grothendieck construction

Given a scaled simplicial set $S$ we construct a 2-categorical version of the
straightening-unstraightening adjunction furnishing an equivalence between the
$\infty$-bicategory of outer 2-Cartesian fi

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The Euler Characteristic of Finite Categories

We first assign a quadratic form and in particular a rational number to every
finite category. In some cases, we call this rational number the Euler
characteristic of the category. We show that this e

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A monoidal Grothendieck construction for $\infty$-categories

We construct a monoidal version of Lurie's un/straightening equivalence. In
more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow
the $\infty$-category of coCartesian fibrati

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Yoneda's lemma for internal higher categories

We develop some basic concepts in the theory of higher categories internal to
an arbitrary $\infty$-topos. We define internal left and right fibrations and
prove a version of the Grothendieck construc

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Cartesian fibrations of simplicial presheaves

Yoneda Lemma for $\mathcal{D}$-Simplicial Spaces

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A Construction of the Monoidal Envelope of in the Model of Segal Dendroidal Spaces

Monoidal envelopes and Grothendieck construction for dendroidal Segal objects

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A Categorical Semantics for Guarded Petri Nets

We build on the correspondence between Petri nets and free symmetric strict
monoidal categories already investigated in the literature, and present a
categorical semantics for Petri nets with guards.

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The Operadic Nerve, Relative Nerve, and the Grothendieck Construction

We relate the relative nerve $\mathrm{N}_f(\mathcal{D})$ of a diagram of
simplicial sets $f \colon \mathcal{D} \to \mathsf{sSet}$ with the Grothendieck
construction $\mathsf{Gr} F$ of a simplicial fun

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Coherence for bicategories, lax functors, and shadows

Coherence theorems are fundamental to how we think about monoidal categories
and their generalizations. In this paper we revisit Mac Lane's original proof
of coherence for monoidal categories using th

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On Hofmann-Streicher universes

We have another look at the construction by Hofmann and Streicher of a
universe $(U,{\mathsf{E}l})$ for the interpretation of Martin-L\"of type theory
in a presheaf category $\hat{\mathbb{C}}$. It tur

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A generalisation of a Groteck construction to the setting of sites

Sheaves on Grothendieck constructions

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Nerves and classifying spaces for bicategories

This paper explores the relationship amongst the various simplicial and
pseudo-simplicial objects characteristically associated to any bicategory C. It
proves the fact that the geometric realizations

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Added to collectionTop 100 Papers By Signal Trends

2-Dimensional Categories

This book is an introduction to 2-categories and bicategories, assuming only
the most elementary aspects of category theory. A review of basic category
theory is followed by a systematic discussion of

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Fibred 2-categories and bicategories

We generalise the usual notion of fibred category; first to fibred
2-categories and then to fibred bicategories. Fibred 2-categories correspond to
2-functors from a 2-category into 2-Cat. Fibred bicat

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Lens Theory

Generalized Lens Categories via functors $\mathcal{C}^{\rm op}\to\mathsf{Cat}$

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