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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

2 votes
1 answer
659 views

How to define 0-sphere in a category with zero object?

The 0-sphere $S^0$ is the coproduct of two points, $$S^0 \simeq \ast \sqcup \ast$$ How to define 0-sphere in a category with zero object? Let $\mathcal{C}$ be a category. A cylinder, $\mathbf{I}$, on …
5 votes
2 answers
1k views

Suspensions are H-cogroup objects

Do you know any reference where you have a formal justification for the following statement that appears in nLab? https://ncatlab.org/nlab/show/suspensions+are+H-cogroup+objects "Let $\mathcal{C}$ b …