Categories of functors between categories with partial morphisms

Hans-Jürgen Vogel

Discussiones Mathematicae - General Algebra and Applications (2005)

  • Volume: 25, Issue: 1, page 39-87
  • ISSN: 1509-9415

Abstract

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It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.

How to cite

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Hans-Jürgen Vogel. "Categories of functors between categories with partial morphisms." Discussiones Mathematicae - General Algebra and Applications 25.1 (2005): 39-87. <http://eudml.org/doc/287644>.

@article{Hans2005,
abstract = {It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.},
author = {Hans-Jürgen Vogel},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {symmetric monoidal category; dhts-category; Hoehnke category; Hoehnke theory; monoidal functor; d-monoidal functor; dht-symmetric functor; functor composition; cartesian product; -category; Hoehnke category: Hoehnke theory; -monoidal functor; -symmetric functor; Cartesian product},
language = {eng},
number = {1},
pages = {39-87},
title = {Categories of functors between categories with partial morphisms},
url = {http://eudml.org/doc/287644},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Hans-Jürgen Vogel
TI - Categories of functors between categories with partial morphisms
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2005
VL - 25
IS - 1
SP - 39
EP - 87
AB - It is well-known that the composition of two functors between categories yields a functor again, whenever it exists. The same is true for functors which preserve in a certain sense the structure of symmetric monoidal categories. Considering small symmetric monoidal categories with an additional structure as objects and the structure preserving functors between them as morphisms one obtains different kinds of functor categories, which are even dt-symmetric categories.
LA - eng
KW - symmetric monoidal category; dhts-category; Hoehnke category; Hoehnke theory; monoidal functor; d-monoidal functor; dht-symmetric functor; functor composition; cartesian product; -category; Hoehnke category: Hoehnke theory; -monoidal functor; -symmetric functor; Cartesian product
UR - http://eudml.org/doc/287644
ER -

References

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  26. [26] H.-J. Vogel, Algebraic theories for Birkhoff-algebras, to appear. 

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