# Golden Integral Calculus By N P Bali ((BETTER)) Golden Integral Calculus By N P Bali

N P Bali Book Integral Calculus By N P BaliQ:

What is a monomorphism?

I just started to study topology and i came across monomorphism for the first time. I have googled but couldn’t find a good explanation.
Can you please explain what a monomorphism is and in which situation we use it?

A:

$\mathcal{C}$ is a category with an initial object $0$ and $\mathcal{A}$ a category.
A monomorphism in $\mathcal{C}$ is a function $f\colon X\to Y$ such that for all $f’\colon X’\to Y$ it holds that $f’=f$ (the domain and codomain agree).
The canonical example is $X\hookrightarrow \emptyset$ and $X\to\{0\}$.
Now we can start thinking about some natural categories that contain monomorphisms:

The category $\mathcal{P}_f(\mathbb{N})$ of non-empty finite sets has all finite monomorphisms.
In $\mathcal{P}_f(\mathbb{R})$ one can take the initial object $[0,1]$ with its inclusion to $\mathbb{R}$.
In $\mathcal{P}_f(X)$ for any topological space $X$ you can take the identity map $X\to X$ or $X\to \{0\}$.

If you can describe a general purpose definition of a monomorphism you can google for it.

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“Golden Integral Calculus : N. P. Bali ”

Real Analysis By Np Bali Book

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What are the topics of this book?
Innovative solutions of elementary problems in mathematics.
Integral Calculus – Inverse Functionality of the Derivative and the Chain rule.
Differential Equations – With analytic solutions.
Difference and Differential Equations – That are solved analytically.
Vector Calculus – Magnetic fields and fluxes through the surface of a magnet.
Vector fields and differential forms.
Coordinate Geometry – Integration and differentiation of a vector with respect to a variable.
Vector Fields and Calculus of Variations.
Vector Fields, Fluxes, and Vortex Rings.
Vector fields, integral calculus, Flux and Vortex Rings.
Vector Fields, Flux, Integral Calculus, and Flux Knots.
Vector Fields, Calculus of Variations, and Flux Rings.
Vector fields, Flux, Calculus of Variations, and Flux Knots.
Integral Calculus, Calculus of Variations, Flux Rings, Flux Knots, and Flux.
The book addresses to the topics in the questions of the previous exam.I had already studied the topics and solved problems in the past exam questions.The topics in the book and previous examination are same.
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