nLab
cartesian functor

Context

Monoidal categories

With symmetry

With duals for objects

  • (list of them)

  • (what they have)

  • , a.k.a.

  • , a.k.a.

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

  • (, , , )

Internal monoids

Examples

Theorems

In higher category theory

Category theory

Concepts

Universal constructions

    • /

    • /

Theorems

Extensions

Applications

Contents

Definition

The phrase cartesian functor has been used in category theory with several different (but related) meanings.

Because of this ambiguity, it is perhaps always better to use a more precise term such as “(strong) morphism of fibrations”, “cartesian monoidal functor” or “finite product preserving functor”, and “finitely continuous functor” or “lex functor”.

Last revised on January 22, 2013 at 19:33:52. See the history of this page for a list of all contributions to it.