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YCor
YCor
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Are Strict Higher Categories More General Than Weak Higher Categoriesstrict higher categories more general than weak higher categories?

I've been exploring the differences between strict and weak higher categories, and I'm curious about their expressiveness and generality. In strict higher categories, morphisms and coherence are explicitly defined at each level, which seems to offer a more comprehensive framework.

My Questionsquestions:

  • Do strict higher categories provide a more general framework than weak categories because they allow explicit definitions that can encompass weak behaviors?

  • How does the complexity of strict categories compare to the flexibility of weak categories in terms of modeling mathematical structures?

  • Can strict categories inherently express more due to their explicit nature, or does the homotopy equivalence in weak categories offer a fundamentally different form of expressiveness?

  • If strict higher categories are able to capture more fine grained detail that is lost in homotopical approach, why is it less used? Is it because working with strict higher category theory would uncover more details, but it would be too hard?

Are Strict Higher Categories More General Than Weak Higher Categories?

I've been exploring the differences between strict and weak higher categories, and I'm curious about their expressiveness and generality. In strict higher categories, morphisms and coherence are explicitly defined at each level, which seems to offer a more comprehensive framework.

My Questions:

  • Do strict higher categories provide a more general framework than weak categories because they allow explicit definitions that can encompass weak behaviors?

  • How does the complexity of strict categories compare to the flexibility of weak categories in terms of modeling mathematical structures?

  • Can strict categories inherently express more due to their explicit nature, or does the homotopy equivalence in weak categories offer a fundamentally different form of expressiveness?

  • If strict higher categories are able to capture more fine grained detail that is lost in homotopical approach, why is it less used? Is it because working with strict higher category theory would uncover more details, but it would be too hard?

Are strict higher categories more general than weak higher categories?

I've been exploring the differences between strict and weak higher categories, and I'm curious about their expressiveness and generality. In strict higher categories, morphisms and coherence are explicitly defined at each level, which seems to offer a more comprehensive framework.

My questions:

  • Do strict higher categories provide a more general framework than weak categories because they allow explicit definitions that can encompass weak behaviors?

  • How does the complexity of strict categories compare to the flexibility of weak categories in terms of modeling mathematical structures?

  • Can strict categories inherently express more due to their explicit nature, or does the homotopy equivalence in weak categories offer a fundamentally different form of expressiveness?

  • If strict higher categories are able to capture more fine grained detail that is lost in homotopical approach, why is it less used? Is it because working with strict higher category theory would uncover more details, but it would be too hard?

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Pan Mrož
Pan Mrož
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Are Strict Higher Categories More General Than Weak Higher Categories?

I've been exploring the differences between strict and weak higher categories, and I'm curious about their expressiveness and generality. In strict higher categories, morphisms and coherence are explicitly defined at each level, which seems to offer a more comprehensive framework.

My Questions:

  • Do strict higher categories provide a more general framework than weak categories because they allow explicit definitions that can encompass weak behaviors?

  • How does the complexity of strict categories compare to the flexibility of weak categories in terms of modeling mathematical structures?

  • Can strict categories inherently express more due to their explicit nature, or does the homotopy equivalence in weak categories offer a fundamentally different form of expressiveness?

  • If strict higher categories are able to capture more fine grained detail that is lost in homotopical approach, why is it less used? Is it because working with strict higher category theory would uncover more details, but it would be too hard?