Draft:Yoneda extension (kan extension)
Wikipedia - Recent changes [en] - Saturday, April 25, 2026
← Previous revision
Revision as of 08:29, 25 April 2026
Line 1:
Line 1:
Let <math>\mathcal{C}</math> a small category and <math>F:\mathcal{C} \rightarrow \mathcal{D}</math> a functor, its Yoneda extension
Let <math>\mathcal{C}</math> a small category and <math>F:\mathcal{C} \rightarrow \mathcal{D}</math> a functor, its Yoneda extension
<math>\tilde F:[\mathcal{C}^{op},\mathbf{Set}] \rightarrow \mathcal{D}</math> is the left Kan extension <math>\tilde F:[\mathcal{C}^{op},\mathbf{Set}] \rightarrow \mathcal{D}</math>
Lan is the left Kan extension <math>\mathrm{Lan}_{H^{\bullet}} F<math> Y
F : [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right]
<math>\tilde F:[\mathcal{C}^{op},\mathbf{Set}] \rightarrow \mathcal{D}</math> is the left Kan extension <math>\tilde F:[\mathcal{C}^{op},\mathbf{Set}] \rightarrow \mathcal{D}</math>
Lan is the left Kan extension <math>\mathrm{Lan}_{H^{\bullet}} F<math> Y
F : [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right] [\mathcal{C}^{op},\mathbf{Set}\right]