Direct products in a category of funcoids

ADDED: I’ve proved that subatomic productPlanetmathPlanetmathPlanetmath is the categorical product.

There are defined (\href my book) several kinds of product of (any possibly infiniteMathworldPlanetmath number) funcoids:

  1. 1.

    cross-composition product

  2. 2.

    subatomic product

  3. 3.

    displaced product

There is one more kind of product, for which it is not proved that the product of funcoids are (pointfree) funcoids:


It is considered natural by analogyMathworldPlanetmath with the category Top of topological spacesMathworldPlanetmath to consider this category:

  • Objects are endofuncoids on small sets.

  • Morphisms between a endofuncoids μ and ν are continuousPlanetmathPlanetmath (that is corresponding to a continuous funcoid) functions from the object of μ to the object of ν.

  • CompositionMathworldPlanetmath is induced by composition of functions.

It is trivial to show that the above is really a category.

The product of functions is the same as in Set.

Title Direct products in a category of funcoids
Canonical name DirectProductsInACategoryOfFuncoids
Date of creation 2013-09-12 19:40:35
Last modified on 2013-09-12 19:40:35
Owner porton (9363)
Last modified by porton (9363)
Numerical id 11
Author porton (9363)
Entry type Definition
Classification msc 54J05
Classification msc 54A05
Classification msc 54D99
Classification msc 54E05
Classification msc 54E17
Classification msc 54E99