nLab
homotopy-homology-cohomology

	homotopy	cohomology	homology
	$[S^n,-]$	$[-,A]$	$(-)\otimes A$
category theory	covariant hom	contravariant hom	tensor product
homological algebra	Ext	Ext	Tor
enriched category theory	end	end	coend
homotopy theory	derived hom space $ℝ\mathrm{Hom}(S^n,-)$	cocycles $ℝ\mathrm{Hom}(-,A)$	derived tensor product $(-){\otimes }^{𝕃}A$