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Lemme de Yoneda pour les foncteurs à valeurs monoidales

Fethi Kadhi

Abstract

We consider a closed symmetric monoidal category $\mathcal{M}$. We show that if $I$ is a small category then $\mathcal{M}^I$ is a closed $\mathcal{M}$-module. We rewrite the Yoneda Lemma in the case of monoidal valued functors. We derive an adjoint functor theorem and we show that $\mathcal{M}^I$ is a closed symmetric monoidal category

Lemme de Yoneda pour les foncteurs à valeurs monoidales

Abstract

We consider a closed symmetric monoidal category . We show that if is a small category then is a closed -module. We rewrite the Yoneda Lemma in the case of monoidal valued functors. We derive an adjoint functor theorem and we show that is a closed symmetric monoidal category

Paper Structure

This paper contains 5 sections, 47 equations.

Table of Contents

  1. Introduction
  2. Catégories monoïdales
  3. Structure de $\mathscr{M}$- module
  4. Lemme de Yoneda pour les catégories monoïdales
  5. Théorème de foncteur adjoint

Theorems & Definitions (8)

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