Objects of categories as complex numbers

@article{Fiore2002ObjectsOC,
  title={Objects of categories as complex numbers},
  author={Marcelo P. Fiore and Tom Leinster},
  journal={Advances in Mathematics},
  year={2002},
  volume={190},
  pages={264-277}
}

Algebra of Trees

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

An objective representation of the Gaussian integers

On analytic groupoid cardinality

  • J. Fullwood
  • Mathematics
    European 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

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)

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

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

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

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

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

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

Seven trees in one

Isomorphisms of generic recursive polynomial types

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

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

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

Negative sets have Euler characteristic and dimension

Some thoughts on the future of category theory