Cote n° 106 · pages 1–15 · 26 displayed formulas · [Champs (stacks) 3] : notes manuscrites (s.d.).
Inventory dating : [à partir de 1982]
Édition de démonstration

batch 1 · p. 1 — read it beside the facsimile1 / 26 · 6 distinct symbols, 19 written
\[W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}} \longrightarrow W^{-1}\mathcal{C}\]
LaTeX source
\[
W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}} \longrightarrow W^{-1}\mathcal{C}
\]
batch 1 · p. 1 — read it beside the facsimile2 / 26 · 7 distinct symbols, 40 written
\[\Phi : W^{-1}\mathcal{C} \longrightarrow W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}}, \qquad \text{i.e.\ } \mathcal{C} \longrightarrow W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}}\]
LaTeX source
\[
\Phi : W^{-1}\mathcal{C} \longrightarrow
W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}},
\qquad \text{i.e.\ } \mathcal{C} \longrightarrow
W_{\mathrm{cof}}^{-1}\mathcal{C}_{\mathrm{cof}}
\]
batch 1 · p. 1 — read it beside the facsimile3 / 26 · 15 distinct symbols, 41 written
\[[i]^{-1}\widetilde{f} : \widetilde{x} \longrightarrow \widetilde{y} \qquad \text{dans } \mathrm{Hom}_{W_{\mathrm{cof}}^{-1} \mathcal{C}_{\mathrm{cof}}}(\widetilde{x}, \widetilde{y}).\]
LaTeX source
\[
[i]^{-1}\widetilde{f} : \widetilde{x} \longrightarrow \widetilde{y}
\qquad \text{dans } \mathrm{Hom}_{W_{\mathrm{cof}}^{-1}
\mathcal{C}_{\mathrm{cof}}}(\widetilde{x}, \widetilde{y}).
\]
batch 1 · p. 3 — read it beside the facsimile4 / 26 · 13 distinct symbols, 25 written
\[R \overset{\text{déf}}{=} \Psi\Phi|\mathcal{C}, \qquad x \longmapsto \widetilde{x}, \qquad \mathcal{C} \longrightarrow W^{-1}\mathcal{C}\]
LaTeX source
\[
R \overset{\text{déf}}{=} \Psi\Phi|\mathcal{C},
\qquad x \longmapsto \widetilde{x},
\qquad \mathcal{C} \longrightarrow W^{-1}\mathcal{C}
\]
batch 1 · p. 3 — read it beside the facsimile5 / 26 · 10 distinct symbols, 14 written
\[R(x) = \widetilde{x} \overset{[\alpha_x]}{\longrightarrow} x\]
LaTeX source
\[
R(x) = \widetilde{x} \overset{[\alpha_x]}{\longrightarrow} x
\]
batch 1 · p. 3 — read it beside the facsimile6 / 26 · 13 distinct symbols, 26 written
\[[\alpha_y]\,\bigl([i_f]^{-1}[\widetilde{f}]\bigr) = [f]\,[\alpha_x].\]
LaTeX source
\[
[\alpha_y]\,\bigl([i_f]^{-1}[\widetilde{f}]\bigr) = [f]\,[\alpha_x].
\]
batch 1 · p. 3 — read it beside the facsimile7 / 26 · 8 distinct symbols, 26 written
\[[\beta_f \widetilde{f}] = [f\alpha_x] = [f][\alpha_x] \qquad \text{cqfd.}\]
LaTeX source
\[
[\beta_f \widetilde{f}] = [f\alpha_x] = [f][\alpha_x]
\qquad \text{cqfd.}
\]
batch 1 · p. 5 — read it beside the facsimile8 / 26 · 8 distinct symbols, 31 written
\[\underline{Ch}_0(x,y) = \text{catégorie des diagrammes}\]
LaTeX source
\[
\underline{Ch}_0(x,y) = \text{catégorie des diagrammes}
\]
batch 1 · p. 5 — read it beside the facsimile9 / 26 · 14 distinct symbols, 35 written
\[\underline{Ch}_0(x,y) \times \underline{Ch}_0(y,z) \longrightarrow \underline{Ch}_0(x,z), \qquad (F, G) \longmapsto G \cdot F\]
LaTeX source
\[
\underline{Ch}_0(x,y) \times \underline{Ch}_0(y,z) \longrightarrow
\underline{Ch}_0(x,z),
\qquad (F, G) \longmapsto G \cdot F
\]
batch 1 · p. 5 — read it beside the facsimile10 / 26 · 11 distinct symbols, 18 written
\[(g,j) \circ (f,i) = (g'g) \cdot \uncertain{k_y}\]
LaTeX source
\[
(g,j) \circ (f,i) = (g'g) \cdot \uncertain{k_y}
\]
batch 1 · p. 7 — read it beside the facsimile11 / 26 · 14 distinct symbols, 37 written
\[\underline{\mathrm{Hom}}_{\mathcal{C}}(x,y)_{\text{discret}} \longrightarrow \underline{Ch}_0(x,y), \qquad f \longmapsto (f, 1d_x)\]
LaTeX source
\[
\underline{\mathrm{Hom}}_{\mathcal{C}}(x,y)_{\text{discret}}
\longrightarrow \underline{Ch}_0(x,y),
\qquad f \longmapsto (f, 1d_x)
\]
batch 1 · p. 7 — read it beside the facsimile12 / 26 · 9 distinct symbols, 25 written
\[\pi_0(x,y) \overset{\text{déf}}{=} \pi_0\bigl(\underline{Ch}_0(x,y)\bigr),\]
LaTeX source
\[
\pi_0(x,y) \overset{\text{déf}}{=} \pi_0\bigl(\underline{Ch}_0(x,y)\bigr),
\]
batch 1 · p. 7 — read it beside the facsimile13 / 26 · 3 distinct symbols, 6 written
\[\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}.\]
LaTeX source
\[
\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}.
\]
batch 1 · p. 7 — read it beside the facsimile14 / 26 · 12 distinct symbols, 39 written
\[(gf, i) \in \text{comp.\ conn.\ de } \underline{1}_x \text{ dans } \pi_0\bigl(\underline{Ch}_0(x,x)\bigr)\]
LaTeX source
\[
(gf, i) \in \text{comp.\ conn.\ de } \underline{1}_x
\text{ dans } \pi_0\bigl(\underline{Ch}_0(x,x)\bigr)
\]
batch 1 · p. 9 — read it beside the facsimile15 / 26 · 5 distinct symbols, 5 written
\[\alpha g = 1_y.\]
LaTeX source
\[
\alpha g = 1_y.
\]
batch 1 · p. 9 — read it beside the facsimile16 / 26 · 15 distinct symbols, 28 written
\[q : \widetilde{\mathcal{C}} \longrightarrow W^{-1}\mathcal{C}, \qquad x \longmapsto x, \qquad (f,i) \longmapsto [i]^{-1}[f]\]
LaTeX source
\[
q : \widetilde{\mathcal{C}} \longrightarrow W^{-1}\mathcal{C},
\qquad x \longmapsto x,
\qquad (f,i) \longmapsto [i]^{-1}[f]
\]
batch 1 · p. 9 — read it beside the facsimile17 / 26 · 9 distinct symbols, 16 written
\[[f]\,[i]^{-1}[g] = [1_y],\]
LaTeX source
\[
[f]\,[i]^{-1}[g] = [1_y],
\]
batch 1 · p. 11 — read it beside the facsimile18 / 26 · 6 distinct symbols, 9 written
\[\widetilde{\mathcal{C}} \longrightarrow W^{-1}\mathcal{C}\]
LaTeX source
\[
\widetilde{\mathcal{C}} \longrightarrow W^{-1}\mathcal{C}
\]
batch 1 · p. 11 — read it beside the facsimile19 / 26 · 5 distinct symbols, 9 written
\[W_0 = W \cap \mathrm{cof}.\]
LaTeX source
\[
W_0 = W \cap \mathrm{cof}.
\]
batch 1 · p. 13 — read it beside the facsimile20 / 26 · 8 distinct symbols, 13 written
\[F = [f], \qquad G = [1_y, f]\]
LaTeX source
\[
F = [f], \qquad G = [1_y, f]
\]
batch 1 · p. 13 — read it beside the facsimile21 / 26 · 3 distinct symbols, 6 written
\[\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}\]
LaTeX source
\[
\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}
\]
batch 1 · p. 13 — read it beside the facsimile22 / 26 · 3 distinct symbols, 4 written
\[\alpha f' = f\]
LaTeX source
\[
\alpha f' = f
\]
batch 1 · p. 15 — read it beside the facsimile23 / 26 · 5 distinct symbols, 6 written
\[f''_0 = \varphi_0\, g.\]
LaTeX source
\[
f''_0 = \varphi_0\, g.
\]
batch 1 · p. 15 — read it beside the facsimile24 / 26 · 7 distinct symbols, 12 written
\[u : (f_0, \alpha) \longrightarrow (f''_0, \alpha'')\]
LaTeX source
\[
u : (f_0, \alpha) \longrightarrow (f''_0, \alpha'')
\]
batch 1 · p. 15 — read it beside the facsimile25 / 26 · 11 distinct symbols, 23 written
\[[f_0, i] = [\mathrm{id}_{\bar{y}}, i] \circ (f, \mathrm{id}_{\bar{y}}),\]
LaTeX source
\[
[f_0, i] = [\mathrm{id}_{\bar{y}}, i] \circ (f, \mathrm{id}_{\bar{y}}),
\]
batch 1 · p. 15 — read it beside the facsimile26 / 26 · 3 distinct symbols, 6 written
\[\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}.\]
LaTeX source
\[
\mathcal{C} \longrightarrow \widetilde{\mathcal{C}}.
\]