# Tensors, Monads And Actions

@article{Seal2012TensorsMA, title={Tensors, Monads And Actions}, author={Gavin J. Seal}, journal={Theory and Applications of Categories}, year={2012}, volume={28}, pages={403-433} }

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base category C.

## 22 Citations

### Monads on Higher Monoidal Categories

- MathematicsAppl. Categorical Struct.
- 2018

The structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad are identified.

### Polynomial and Analytic Functors and Monads, revisited

- Mathematics
- 2015

We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.

### The formal theory of multimonoidal monads

- Mathematics
- 2018

Certain aspects of Street’s formal theory of monads in 2-categories are extended to multimonoidal monads in strict symmetric monoidal 2-categories. Namely, any strict symmetric monoidal 2-category M…

### Monads on Higher Monoidal Categories

- MathematicsApplied Categorical Structures
- 2017

We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the…

### The formal theory of multimonoidal monads

- Mathematics
- 2018

Certain aspects of Street's formal theory of monads in 2-categories are extended to multimonoidal monads in symmetric strict monoidal 2-categories. Namely, any symmetric strict monoidal 2-category…

### Tensor categorical foundations of algebraic geometry

- Mathematics
- 2014

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this…

### MODEL CATEGORIES: THEORY AND APPLICATIONS

- Mathematics
- 2016

This paper consists of two interlaced – but mathematically independent – parts. In the first, we briefly introduce the theory of model categories and its uses. This tour culminates in a proof of a…

### Modules over Monads and Operational Semantics

- Computer Science, MathematicsFSCD
- 2020

This paper generalises the reduction monads of Ahrens et al., and introduces transition monads, thus covering new applications such as λμ-calculus, π- Calculus, Positive GSOS specifications, differential λ-Calculus, and the big-step, simply-typed, call-by-value λ -calculus.

### LNL polycategories and doctrines of linear logic

- MathematicsArXiv
- 2021

It is shown that free algebras for LNL doctrines can be presented by a sequent calculus, and that every morphism of doctrines induces an adjunction between their 2-categories of alge bras.

## References

SHOWING 1-10 OF 25 REFERENCES

### Monads on symmetric monoidal closed categories

- Mathematics
- 1970

This note is concerned with "categories with internal horn and | and we shall use the terminology from the paper [2] by EIL~.NBERG and Kv.Imy. The result proved may be stated briefly as follows : a…

### MONAD COMPOSITIONS I: GENERAL CONSTRUCTIONS AND RECURSIVE DISTRIBUTIVE LAWS

- Mathematics
- 2007

New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product mon- ads, recursively-defined distributive laws, and linear equations.…

### Strong functors and monoidal monads

- Mathematics
- 1972

In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, taken…

### Tensor Products and Bimorphisms

- MathematicsCanadian Mathematical Bulletin
- 1976

The binary tensor product, for modules over a commutative ring, has two different aspects: its connection with universal bilinear maps and its adjointness to the internal hom-functor. Furthermore, in…

### Closed categories generated by commutative monads

- MathematicsJournal of the Australian Mathematical Society
- 1971

The notion of commutative monad was defined by the author in [4]. The content of the present paper may briefly be stated: The category of algebras for a commutative monad can in a canonical way be…

### REVIEWS-Sketches of an elephant: A topos theory compendium

- Mathematics
- 2003

A1 Regular and Cartesian Closed Categories A2 Toposes - Basic Theory A3 Allegories A4 Geometric Morphisms - Basic Theory B1 Fibrations and Indexed Categories B2 Internal and Locally Internal…

### The structure of Galois connections.

- Mathematics
- 1974

This paper deals with Galois connections between two partially ordered sets (posets) A, B. The first sections are devoted to the construction of all Galois connections between A and B. The last…

### Abstract and Concrete Categories - The Joy of Cats

- Mathematics
- 1990

This chapter discusses Categories and Functors, Topological Categories, Partial Morphisms, Quasitopoi, and Topological Universes, as well as partial Morphisms in Abstract Categories and Cartesian Closed Categories.

### Tenseurs et machines

- Mathematics
- 1980

© Andrée C. Ehresmann et les auteurs, 1980, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les…