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DamienC
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This might be a naive answer but here is a suggestion for the definition of $\pi_n$-fibrations: maps having the RLP with respect to the the map $\Delta^k\to\Delta^k\times I$ for any $\leq n$$k\leq n$.

In the limit you will get the "obvious" fibrant-object structure on $Top$ which comes from its usual model structure (recall that the full subcategory of fibrant objects in any model category is a category of fibrant objects.. and that all objects are fibrants in $Top$).

This might be a naive answer but here is a suggestion for the definition of $\pi_n$-fibrations: maps having the RLP with respect to the the map $\Delta^k\to\Delta^k\times I$ for any $\leq n$.

In the limit you will get the "obvious" fibrant-object structure on $Top$ which comes from its usual model structure (recall that the full subcategory of fibrant objects in any model category is a category of fibrant objects.. and that all objects are fibrants in $Top$.

This might be a naive answer but here is a suggestion for the definition of $\pi_n$-fibrations: maps having the RLP with respect to the the map $\Delta^k\to\Delta^k\times I$ for any $k\leq n$.

In the limit you will get the "obvious" fibrant-object structure on $Top$ which comes from its usual model structure (recall that the full subcategory of fibrant objects in any model category is a category of fibrant objects.. and that all objects are fibrants in $Top$).

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DamienC
  • 8.4k
  • 1
  • 50
  • 91

This might be a naive answer but here is a suggestion for the definition of $\pi_n$-fibrations: maps having the RLP with respect to the the map $\Delta^k\to\Delta^k\times I$ for any $\leq n$.

In the limit you will get the "obvious" fibrant-object structure on $Top$ which comes from its usual model structure (recall that the full subcategory of fibrant objects in any model category is a category of fibrant objects.. and that all objects are fibrants in $Top$.