# Questions tagged [slice-category]

For questions regarding slice categories.

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### Meaning of being isomorphic over/under $c$ in category theory

To the point: What does being isomorphic over/under an object $c$ mean? Let $x,y,c$ be objects in a categoy $\mathsf C$, and let's concentrate on "over". I think "$x\cong y$ over $c$&...
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### Intuition for comma category and slice category? [closed]

As usual, I am not happy with the definitions until I dont gain some intuition. Could you help me and maybe provide some examples of the concepts? Thank you! My questions are: 1 Comma category = "...
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### What does a morphism in the category $\mathsf{C}_{\alpha, \beta}$ correspond to?

Start with a given category $\mathsf{C}$ and fix two morphisms $\alpha: A \to C$ and $\beta: B \to C$. Consider the category $\mathsf{C}_{\alpha, \beta}$ as follows: Does a morphism in this ...
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### Completeness of over category (slice)

Let $\mathcal J$ be a (small) category (denote $I:= \mathcal J_0$) and $\mathcal C$ a category that has all (small) limits (all limits of shape $\mathcal J$ for all $\mathcal J$). Prop 3.4 states then ...
1 vote
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### How to find initial object of the category of pointed rings?

I have the category of pointed rings. Objects are all pairs $(R, r)$ where $R$ - ring (with 1) and r is the element of R. Morphisms are homomorphism of rings. Morphism $(R, r) \longrightarrow (R', r')$...
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### An elementary question about slice categories

I'm just beginning to dabble into some category theory (from Aluffi's Algebra) and I have some difficulty with morphisms in a slice category. Particularly, I can't see why the diagram of a morphism ...
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### $\Pi_f$ for a morphism $f$ between simplicial sets

This nLab article says presheaf categories (including $\mathsf{sSet}$, the category of simplicial sets) are locally cartesian closed. For presheaf categories, it can be proven by use of the category ...
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### fibered category definition

Im reading Vistolis "Notes on Grothendieck topologies, fibered categories and descent theory", and when i read the definition of a fibered category, it struck me as very similiar to the definition of ...