# A 2-categorical pasting theorem

@article{Power1990A2P,
title={A 2-categorical pasting theorem},
author={A. J. Power},
journal={Journal of Algebra},
year={1990},
volume={129},
pages={439-445}
}
• A. Power
• Published 1 March 1990
• Mathematics
• Journal of Algebra
126 Citations
Describing free $\omega$ -categories
• Computer Science
2019 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
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.
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
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
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
• J. Baez
• Mathematics
Category 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
• Mathematics
18th 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
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
• J. Power
• Mathematics
Mathematical 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