let & be a connected category and h: Z-X andfXY.9Prove that if f and gouch that f‡g,2. Dualise (1) and prove1.are constant#goh.the result inthen foh #morphismsdualforen.

Given that:Let be a connected category and such that .To prove: If f and g are constant morphisms…

Answered: 1. Let & be a connected category and hi…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

let & be a connected category and h: Z-X and
f
X
Y.
9
Prove that if f and g
ouch that f‡g,
2. Dualise (1) and prove
1.
are constant
#goh.
the result in
then foh #
morphisms
dual
foren.

Expert Solution

Step 1: Introduction

Given that:

Let $sigma$ be a connected category and $h colon Z rightwards arrow X$ such that $X rightwards arrow from g to f of Y$ .

To prove: If f and g are $sigma$ constant morphisms such that $f not equal to g$ then $f ring operator h not equal to g ring operator h$ .

Concept:

Definition of σ-Constant Isomorphisms:

In a category σ, a σ-constant isomorphism is an isomorphism (a morphism with an inverse) that behaves the same way for all objects in the category.

It means that for any objects X and Y in the category σ, if f: X → Y is a σ-constant isomorphism, then for any other objects Z and W in the category, if h: Z → W is a morphism, f behaves the same way for all pairs of objects (X, Y), (Z, W) in the category.