I've heard some people saying that it would be easier to study homotopy theory first through simplicial sets. First, i thought that these people were not being serious. But it caught me wondering...

It's not a secret that nowadays homotopy theory is not just a branch of algebraic topology, it's a actually an enourmous mathematical field of research subsuming category theory, homological algebra and having deep connections with algebraic geometry and commutative algebra.

I wonder if it's worth it to think about introducing homotopy theory as an independent subject, for example, build everything axiomatically relying on a category theory machinery rather than introduct it as a subject of algebraic topology.

I'm not sure such references do exist, maybe, Emily Riehl's book "Categorical homotopy theory" can be thought as a introduction to homotopy theory for category theorists(thought she advises to read on simplicial homotopy theory and homotopy limits and colimits before approaching the book, but says it's not a formal prerequisiste ).

P.G. Goerss, J.F. Jardine "Simplicial homotopy theory" seems to assume algebraic topology, though I haven't seriously researched whether it truly does so.

So, to sum it up, it is a question about both whether such approach can be viable and whether it's already used in some literature. Of course, anything else close to this topic will be appreciated as well.

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