## 16 Citations

### Algebra of Trees

- Philosophy
- 2013

We have seen that classic representations of classifications give hierarchical structures, which are the chains of partitions of a partition lattice. But as we have seen also, such structures may…

### On analytic groupoid cardinality

- MathematicsEuropean Journal of Mathematics
- 2022

Groupoids graded by the groupoid of bijections between ﬁnite sets admit generating functions which encode the groupoid cardinalities of their graded components. As suggested in the work of Baez and…

### Isomorphisms of generic recursive polynomial types

- MathematicsPOPL 2004
- 2004

This paper gives the first decidability results on type isomorphism for recursive types, establishing the explicit decidability of type isomorphism for the type theory of sums and products over an…

### How to Take the Inverse of a Type (Artifact)

- MathematicsDagstuhl Artifacts Ser.
- 2022

In functional programming, regular types are a subset of algebraic data types formed from products and sums with their respective units. One can view regular types as forming a commutative semiring…

### Foundations of categorified representation theory

- Mathematics
- 2010

Author(s): Hoffnung, Alexander | Advisor(s): Baez, John C | Abstract: This thesis develops the foundations of the program of groupoidification and presents an application of this program --- the…

### Groupoidification Made Easy

- Mathematics
- 2008

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed…

### The Hecke Bicategory

- MathematicsAxioms
- 2012

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid—the category of permutation representations of a finite group. As an…

### Physics, Topology, Logic and Computation: A Rosetta Stone

- Physics
- 2009

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology.…

### Compact Closed Bicategories

- Mathematics
- 2013

A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. The unit and counit satisfy the usual "zig-zag" identities of a compact closed category…

## References

SHOWING 1-8 OF 8 REFERENCES

### Isomorphisms of generic recursive polynomial types

- MathematicsPOPL
- 2004

This paper gives the first decidability results on type isomorphism for recursive types, establishing the explicit decidability of type isomorphism for the type theory of sums and products over an…

### On the Structure of Semigroups

- Mathematics
- 1951

The purpose of this paper is to give the basis, and a few fundamental theorems, of a suggested systematic theory of semigroups. By a semigroup is meant a set S closed to a single associative, binary…

### Coherence for distributivity

- Mathematics
- 1972

Miquel L. Laplaza University of Chicago and University of Puerto Rico at Mayaguez Received November 5, 197