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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
5
votes
Is there an additive model of the stable homotopy category?
In the category $Ho(C)$, say that every map is a fibration and a cofibration, and define the weak equivalences to be the isomorphisms. This makes $Ho(C)$ into a model category; its homotopy category i …
8
votes
Constructions unique up to non-unique isomorphism
The homology of a differential graded algebra has an $A_\infty$-algebra structure which is unique up to non-unique isomorphism.
See Keller's nice expository paper Introduction to A-infinity algebras a …