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Framed bicategories and monoidal fibrations

- Michael Shulman
- Mathematics
- 9 June 2007

In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors,… Expand

Univalence for inverse diagrams and homotopy canonicity

- Michael Shulman
- MathematicsMathematical Structures in Computer Science
- 15 March 2012

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Univalent categories and the Rezk completion

- B. Ahrens, Krzysztof Kapulkin, Michael Shulman
- MathematicsMathematical Structures in Computer Science
- 4 March 2013

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Constructing symmetric monoidal bicategories

- Michael Shulman
- Mathematics
- 7 April 2010

We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently… Expand

A type theory for synthetic ∞-categories

- E. Riehl, Michael Shulman
- Mathematics
- 1 February 2018

We propose foundations for a synthetic theory of $(\infty,1)$-categories within homotopy type theory. We axiomatize a directed interval type, then define higher simplices from it and use them to… Expand

A unified framework for generalized multicategories

- G. Cruttwell, Michael Shulman
- Mathematics
- 14 July 2009

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere… Expand

Brouwer's fixed-point theorem in real-cohesive homotopy type theory

- Michael Shulman
- MathematicsMathematical Structures in Computer Science
- 25 September 2015

We combine homotopy type theory with axiomatic cohesion, expressing the latter internally with a version of ‘adjoint logic’ in which the discretization and codiscretization modalities are… Expand

The HoTT library: a formalization of homotopy type theory in Coq

- A. Bauer, Jason Gross, P. Lumsdaine, Michael Shulman, Matthieu Sozeau, Bas Spitters
- MathematicsCPP
- 14 October 2016

We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher… Expand

Shadows and traces in bicategories

- K. Ponto, Michael Shulman
- Mathematics
- 7 October 2009

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some… Expand

Modalities in homotopy type theory

- E. Rijke, Michael Shulman, Bas Spitters
- MathematicsLog. Methods Comput. Sci.
- 22 June 2017

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