## 126 Citations

Describing free $\omega$ -categories

- Computer Science2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

This work first shows that parity complexes do not satisfy the aforementioned freeness property, and proposes a new formalism that satisfies the freenness property and which can be seen as a corrected version of parity complexes.

Describing free ω-categories

- Computer Science
- 2019

This work first shows that parity complexes do not satisfy the aforementioned freeness property, and proposes a new formalism that satisfies the freenness property and which can be seen as a corrected version of parity complexes.

Diagrammatic sets and rewriting in weak higher categories.

- Mathematics
- 2020

We revisit Kapranov and Voevodsky's idea of spaces modelled on combinatorial pasting diagrams, now as a framework for higher-dimensional rewriting and the basis of a model of weak omega-categories.…

Unifying notions of pasting diagrams

- Mathematics
- 2019

In this work, we relate the three main formalisms for the notion of pasting diagram in strict $\omega$-categories: Street's parity complexes, Johnson's pasting schemes and Steiner's augmented…

A $2$-categorical approach to change of base and geometric morphisms I

- Mathematics
- 1991

We introduce a notion of equipment which generalizes the earlier notion of pro-arrow equipment and includes such familiar constructs as relK, spnK, parK ,a nd proK for a suitable category K, along…

Representable diagrammatic sets as a model of weak higher categories

- Mathematics
- 2019

Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose this as a…

Pushouts of Dwyer maps are $(\infty,1)$-categorical

- Mathematics
- 2022

. The inclusion of 1-categories into ( ∞ , 1)-categories fails to pre-serve colimits in general, and pushouts in particular. In this note, we observe that if one functor in a span of categories…

An Introduction to n-Categories

- MathematicsCategory Theory and Computer Science
- 1997

This work surveys various concepts of n-category, with an emphasis on ‘weak’ n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence.

Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes

- Mathematics
- 1997

Abstract We give a definition of weak n -categories based on the theory of operads. We work with operads having an arbitrary set S of types, or “ S -operads,” and given such an operad O , we denote…

Elements of ∞-Category Theory

- Philosophy
- 2022

The language of
∞-categories provides an insightful new way of expressing many
results in higher-dimensional mathematics but can be challenging
for the uninitiated. To explain what exactly an…

## References

SHOWING 1-10 OF 11 REFERENCES

The category-theoretic solution of recursive domain equations

- Mathematics18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
- 1977

The purpose of the present paper is to set up a categorical framework in which the known techniques for solving equations find a natural place, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories.

Formal category theory: adjointness for 2-categories

- Mathematics, Philosophy
- 1974

Categories.- 2-categories.- Bicategories.- Properties of Fun(A,B) and Pseud(A,B).- Properties of 2-comma categories.- Adjoint morphisms in 2-categories.- Quasi-adjointness.

An Algebraic Formulation for Data Refinement

- MathematicsMathematical Foundations of Programming Semantics
- 1989

Hoare's principal mathematical constructions are reviewed and they are mildly reformulated and unified in terms of two principal category theoretic notions: those of an enriched category and monad, also known as a triple.

Combinatorial-geometric aspects of polycategory theory : pasting schemes and higher Bruhat orders (list of results)

- Mathematics
- 1991

© Andree C. Ehresmann et les auteurs, 1991, tous droits reserves. L’acces aux archives de la revue « Cahiers de topologie et geometrie differentielle categoriques » implique l’accord avec les…