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There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

For instance, see section 2 of https://web.archive.org/web/20100610083041/math.uchicago.edu/~eriehl/hocolimits.pdf for the simplicial model category case.

There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

For instance, see section 2 of https://emilyriehl.github.io/files/hocolimits.pdf for the simplicial model category case.

There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

For instance, see section 2 of http://www.math.uchicago.edu/~eriehl/hocolimits.pdf for the simplicial model category case.

There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

For instance, see section 2 of https://web.archive.org/web/20100610083041/math.uchicago.edu/~eriehl/hocolimits.pdf for the simplicial model category case.

There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

There is an analogue, but one should replace coequalizers by geometric realizations (homotopy colimits over Δ^op). If $F : I \to M$ is a diagram in a model category, one has

$$\operatorname{hocolim}_I F = \operatorname{hocolim}_{k \in \Delta^{\operatorname{op}}} \coprod_{i_0 \to \cdots \to i_k \in I} F(i_0).$$

For instance, see section 2 of http://www.math.uchicago.edu/~eriehl/hocolimits.pdf for the simplicial model category case.