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Lectures on generalised cohomology.- On H-spaces and infinite loop spaces.- Functors between categories of vector spaces.- Natural vector bundles.- Several new concepts: Lucid and concordant functors, pre-limits, pre-completeness, the continuous and concordant completions of categories.- The categorical comprehension scheme.- Non-abelian sheaf cohomology by derived functors.- Foncteurs derives et K-theorie.- Relative functorial semantics: Adjointness results.- Minimal subalgebras for dynamic triples.- Categories of spectra and infinite loop spaces.- Homology of squares and factoring of diagrams.